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Erratum to: On the cohomology of the moduli space of parabolic connections manuscripta math. (IF 0.61) Pub Date : 2021-01-15 Yuki Matsubara
In the proof of Theorem 1.1 in Matsubara (2019), there are two mistakes that are explained in Remark 4, and therefore the vanishing of the first and the second cohomologies in Theorem 1.1 is still open.
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Log smooth curves over discrete valuation rings manuscripta math. (IF 0.61) Pub Date : 2021-01-12 Rémi Lodh
We give necessary and sufficient conditions for log smoothness of a proper regular arithmetic surface with smooth geometrically connected generic fibre over a discrete valuation ring with perfect residue field. As an application, we recover known criteria for log smooth reduction of minimal normal crossings models of curves.
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On supersingular loci of Shimura varieties for quaternionic unitary groups of degree 2 manuscripta math. (IF 0.61) Pub Date : 2021-01-02 Yasuhiro Oki
We describe the structure of the supersingular locus of a Shimura variety for a quaternionic unitary similitude group of degree 2 over a ramified odd prime p if the level at p is given by a special maximal compact open subgroup. More precisely, we show that such a locus is purely 2-dimensional, and every irreducible component is birational to the Fermat surface. Furthermore, we have an estimation of
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Log smooth deformation theory via Gerstenhaber algebras manuscripta math. (IF 0.61) Pub Date : 2020-12-23 Simon Felten
We construct a \(k\left[ \!\left[ Q\right] \!\right] \)-linear predifferential graded Lie algebra \(L^{\bullet }_{X_0/S_0}\) associated to a log smooth and saturated morphism \(f_0: X_0 \rightarrow S_0\) and prove that it controls the log smooth deformation functor. This provides a geometric interpretation of a construction in Chan et al. (Geometry of the Maurer-Cartan equation near degenerate Calabi-Yau
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Multiplicities for tensor products on special linear versus classical groups manuscripta math. (IF 0.61) Pub Date : 2020-12-02 Dipendra Prasad, Vinay Wagh
There is a natural bijective correspondence between irreducible (algebraic) selfdual representations of the special linear group with those of classical groups. In this paper, using computations done through the LiE software, we compare tensor product of irreducible selfdual representations of the special linear group with those of classical groups to formulate some conjectures relating the two. More
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Optimal results in Lorentzian Aubry–Mather theory manuscripta math. (IF 0.61) Pub Date : 2020-11-30 Stefan Suhr
This article complements the Lorentzian Aubry–Mather Theory in Suhr (Geom Dedicata 160:91–117, 2012; J Fixed Point Theory Appl 21:71, 2019) by giving optimal multiplicity results for the number of maximal invariant measures. As an application the optimal Lipschitz continuity of the time separation on the Abelian cover is established.
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Bubble solutions for a supercritical polyharmonic Hénon-type equation manuscripta math. (IF 0.61) Pub Date : 2020-11-27 Yuxia Guo, Ting Liu
We consider the following problem involving supercritical exponent and polyharmonic operator: $$\begin{aligned} (-\Delta )^mu=K(|y|)u^{m^*-1+\varepsilon }, \;u>0, \hbox { in } B_1(0), \; u \in {\mathcal {D}}_0^{m,2}(B_1(0)), \end{aligned}$$ where \(B_1(0)\) is the unit ball in \({\mathbb {R}}^{N}\), \(m^*=\frac{2N}{N-2m}\) is the critical exponent,\(\; N\ge 2m+2\), \( m \in {\mathbb {N}}_+\), \(\varepsilon
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Cohomology jump loci of 3-manifolds manuscripta math. (IF 0.61) Pub Date : 2020-11-27 Alexander I. Suciu
The cohomology jump loci of a space X are of two basic types: the characteristic varieties, defined in terms of homology with coefficients in rank one local systems, and the resonance varieties, constructed from information encoded in either the cohomology ring, or an algebraic model for X. We explore here the geometry of these varieties and the delicate interplay between them in the context of closed
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Minimal surfaces in spheres and a Ricci-like condition manuscripta math. (IF 0.61) Pub Date : 2020-11-20 Amalia-Sofia Tsouri, Theodoros Vlachos
We deal with minimal surfaces in spheres that are locally isometric to a pseudoholomorphic curve in a totally geodesic \({\mathbb {S}}^{5}\) in the nearly Kähler sphere \({\mathbb {S}}^6\). Being locally isometric to a pseudoholomorphic curve in \({\mathbb {S}}^5\) turns out to be equivalent to the Ricci-like condition \(\Delta \log (1-K)=6K,\) where K is the Gaussian curvature of the induced metric
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Rational curves on genus-one fibrations manuscripta math. (IF 0.61) Pub Date : 2020-11-17 Fabrizio Anella
In this paper we look for necessary and sufficient conditions for a genus-one fibration to have rational curves. We show that a projective variety with log terminal singularities that admits a relatively minimal genus-one fibration \(X\rightarrow B\) does contain vertical rational curves if and only if it not isomorphic to a finite étale quotient of a product \(\tilde{B}\times E\) over B. Many sufficient
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Bounds of the multiplicity of abelian quotient complete intersection singularities manuscripta math. (IF 0.61) Pub Date : 2020-11-16 Kohsuke Shibata
In this paper we investigate the multiplicity and the log canonical threshold of abelian quotient complete intersection singularities in terms of the notion of special datum. Moreover we give bounds of the multiplicity of abelian quotient complete intersection singularities.
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Flat affine manifolds and their transformations manuscripta math. (IF 0.61) Pub Date : 2020-11-13 A. Medina, O. Saldarriaga, A. Villabon
We give a characterization of flat affine connections on manifolds by means of a natural affine representation of the universal covering of the Lie group of diffeomorphisms preserving the connection. From the infinitesimal point of view, this representation is determined by the 1-connection form and the fundamental form of the bundle of linear frames of the manifold. We show that the group of affine
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On the Cheeger problem for rotationally invariant domains manuscripta math. (IF 0.61) Pub Date : 2020-11-13 Vladimir Bobkov, Enea Parini
We investigate the properties of the Cheeger sets of rotationally invariant, bounded domains \(\Omega \subset \mathbb {R}^n\). For a rotationally invariant Cheeger set C, the free boundary \(\partial C \cap \Omega \) consists of pieces of Delaunay surfaces, which are rotationally invariant surfaces of constant mean curvature. We show that if \(\Omega \) is convex, then the free boundary of C consists
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A motivic local Cauchy-Crofton formula manuscripta math. (IF 0.61) Pub Date : 2020-11-12 Arthur Forey
In this note, we establish a version of the local Cauchy-Crofton formula for definable sets in Henselian discretely valued fields of characteristic zero. It allows to compute the motivic local density of a set from the densities of its projections integrated over the Grassmannian.
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Congruences of Siegel Eisenstein series of degree two manuscripta math. (IF 0.61) Pub Date : 2020-11-11 Takuya Yamauchi
In this paper we study congruences between Siegel Eisenstein series and Siegel cusp forms for \(\mathrm{Sp}_4(\mathbb {Z})\).
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Kummer surfaces associated with group schemes manuscripta math. (IF 0.61) Pub Date : 2020-11-11 Shigeyuki Kondō, Stefan Schröer
We introduce Kummer surfaces \(X={\text {Km}}(C\times C)\) with the group scheme \(G=\mu _2\) acting on the self-product of the rational cuspidal curve in characteristic two. The resulting quotients are normal surfaces having a configuration of sixteen rational double points of type \(A_1\), together with a rational double point of type \(D_4\). We show that our Kummer surfaces are precisely the supersingular
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Erratum to: Finite-dimensional pointed Hopf algebras over finite simple groups of Lie type V. Mixed classes in Chevalley and Steinberg groups manuscripta math. (IF 0.61) Pub Date : 2020-10-16 Nicolás Andruskiewitsch, Giovanna Carnovale, Gastón Andrés García
The article title was originally published with typographical error.
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On ruled surfaces with big anti-canonical divisor and numerically trivial divisors on weak log Fano surfaces manuscripta math. (IF 0.61) Pub Date : 2020-10-03 Rikito Ohta, Shinnosuke Okawa
We investigate the structure of geometrically ruled surfaces whose anti-canonical class is big. As an application we show that the Picard group of a normal projective surface whose anti-canonical class is nef and big is a free abelian group of finite rank.
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The derived category of the abelian category of constructible sheaves manuscripta math. (IF 0.61) Pub Date : 2020-09-30 Owen Barrett
We show that the triangulated category of bounded constructible complexes on an algebraic variety X over an algebraically closed field is equivalent to the bounded derived category of the abelian category of constructible sheaves on X, extending a theorem of Nori to the case of positive characteristic.
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Positive Hermitian curvature flow on complex 2-step nilpotent Lie groups manuscripta math. (IF 0.61) Pub Date : 2020-09-29 Mattia Pujia
We study the positive Hermitian curvature flow of left-invariant metrics on complex 2-step nilpotent Lie groups. In this setting we completely characterize the long-time behaviour of the flow, showing that normalized solutions to the flow subconverge to a non-flat algebraic soliton, in Cheeger–Gromov topology. We also exhibit a uniqueness result for algebraic solitons on such Lie groups.
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Holomorphic $$\text {GL}_2({\mathbb C})$$ GL 2 ( C ) -geometry on compact complex manifolds manuscripta math. (IF 0.61) Pub Date : 2020-09-28 Indranil Biswas, Sorin Dumitrescu
We study holomorphic \(\text {GL}_2({\mathbb {C}})\) and \(\text {SL}_2({\mathbb C})\) geometries on compact complex manifolds.
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Finite-dimensional pointed Hopf algebras over finite 3 simple groups of Lie type V. Mixed classes in Chevalley 4 and Steinberg groups manuscripta math. (IF 0.61) Pub Date : 2020-09-26 Nicolás Andruskiewitsch, Giovanna Carnovale, Gastón Andrés García
We show that all classes that are neither semisimple nor unipotent in finite simple Chevalley or Steinberg groups different from \(\mathbf {PSL}_n(q)\) collapse (i.e. are never the support of a finite-dimensional Nichols algebra). As a consequence, we prove that the only finite-dimensional pointed Hopf algebra whose group of group-like elements is \(\mathbf {PSp}_{2n}(q)\), \(\mathbf {P}{\varvec{\Omega
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Two new embedded triply periodic minimal surfaces of genus 4 manuscripta math. (IF 0.61) Pub Date : 2020-09-24 Daniel Freese, Matthias Weber, A. Thomas Yerger, Ramazan Yol
We add two new 1-parameter families to the short list of known embedded triply periodic minimal surfaces of genus 4 in \(\mathbb {R}^3\). Both surfaces can be tiled by minimal pentagons with two straight segments and three planar symmetry curves as boundary. In one case (which has the appearance of the CLP surface of Schwarz with an added handle) the two straight segments are parallel, while they are
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Classification of separable surfaces with constant Gaussian curvature manuscripta math. (IF 0.61) Pub Date : 2020-09-23 Thomas Hasanis, Rafael López
We classify all surfaces with constant Gaussian curvature K in Euclidean 3-space that can be expressed by an implicit equation of type \(f(x)+g(y)+h(z)=0\), where f, g and h are real functions of one variable. If \(K=0\), we prove that the surface is a surface of revolution, a cylindrical surface or a conical surface, obtaining explicit parametrizations of such surfaces. If \(K\not =0\), we prove that
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Boundary Lipschitz regularity and the Hopf lemma on Reifenberg domains for fully nonlinear elliptic equations manuscripta math. (IF 0.61) Pub Date : 2020-09-22 Yuanyuan Lian, Wenxiu Xu, Kai Zhang
In this paper, we prove the boundary Lipschitz regularity and the Hopf Lemma by a unified method on Reifenberg domains for fully nonlinear elliptic equations. Precisely, if the domain \(\Omega \) satisfies the exterior Reifenberg \(C^{1,\mathrm {Dini}}\) condition at \(x_0\in \partial \Omega \) (see Definition 1.3), the solution is Lipschitz continuous at \(x_0\); if \(\Omega \) satisfies the interior
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New pseudo Einstein metrics on Einstein solvmanifolds manuscripta math. (IF 0.61) Pub Date : 2020-09-22 Hui Zhang, Zaili Yan
A Riemannian Einstein manifold is called an Einstein solvmanifold if there exists a transitive solvable group of isometries. In this short note, we show that every Einstein solvmanifold admits at least one pseudo-Riemannian Einstein metric.
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Algebraicity of special L -values attached to Siegel–Jacobi modular forms manuscripta math. (IF 0.61) Pub Date : 2020-09-22 Thanasis Bouganis, Jolanta Marzec
In this work we obtain algebraicity results on special L-values attached to Siegel–Jacobi modular forms. Our method relies on a generalization of the doubling method to the Jacobi group obtained in our previous work, and on introducing a notion of near holomorphy for Siegel–Jacobi modular forms. Some of our results involve also holomorphic projection, which we obtain by using Siegel–Jacobi Poincaré
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Virtual classes of $$\mathbb {G}_\text {m}$$ G m -gerbes manuscripta math. (IF 0.61) Pub Date : 2020-09-20 F. Qu
We show that a perfect obstruction theory for a \(\mathbb {G}_\text {m}\)-gerbe determines a semi-perfect obstruction theory for its base, which is perfect if the gerbe is quasi-compact and affine-pointed. These results streamline the construction of a semi-perfect obstruction theory for the base, and allow us to relate virtual classes of the gerbe and its base.
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Washington units, semispecial units, and annihilation of class groups manuscripta math. (IF 0.61) Pub Date : 2020-09-07 Cornelius Greither, Radan Kučera
Special units are a sort of predecessor of Euler systems, and they are mainly used to obtain annihilators for class groups. So one is interested in finding as many special units as possible (actually we use a technical generalization called “semispecial”). In this paper we show that in any abelian field having a real genus field in the narrow sense all Washington units are semispecial, and that a slightly
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Mustafin varieties, moduli spaces and tropical geometry manuscripta math. (IF 0.61) Pub Date : 2020-08-24 Marvin Anas Hahn, Binglin Li
Mustafin varieties are flat degenerations of projective spaces, induced by a set of lattices in a vector space over a non-archimedean field. They were introduced by Mustafin (Math USSR-Sbornik 34(2):187, 1978) in the 70s in order to generalise Mumford’s groundbreaking work on the unformisation of curves to higher dimension. These varieties have a rich combinatorial structure as can be seen in pioneering
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On the preimage of a sphere by a polynomial mapping manuscripta math. (IF 0.61) Pub Date : 2020-08-17 Zbigniew Jelonek
Let X be an irreducible complex affine variety of dimension greater than one and let \(f:X \rightarrow \mathbb {C}^m\) be a polynomial mapping. Let \({|}*{|}\) be a semialgebraic norm on \(\mathbb {C}^m.\) Then for R large enough the sets \(f^{-1}(B_R), f^{-1}(S_R), X{\setminus } f^{-1}(B_R)\) are all connected, where \(B_R=\{ z\in \mathbb {C}^m : |z|\le R\}\) and \(S_R=\{ z\in \mathbb {C}^m : |z|
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Contact loci and Hironaka’s order manuscripta math. (IF 0.61) Pub Date : 2020-08-12 A. Bravo, S. Encinas, B. Pascual-Escudero
We study contact loci sets of arcs and the behavior of Hironaka’s order function defined in constructive Resolution of singularities. We show that this function can be read in terms of the irreducible components of the contact loci sets at a singular point of an algebraic variety.
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A Fundamental Class for Intersection Spaces of Depth One Witt Spaces manuscripta math. (IF 0.61) Pub Date : 2020-08-11 Dominik J. Wrazidlo
By a theorem of Banagl–Chriestenson, intersection spaces of depth one pseudomanifolds exhibit generalized Poincaré duality of Betti numbers, provided that certain characteristic classes of the link bundles vanish. In this paper, we show that the middle-perversity intersection space of a depth one Witt space can be completed to a rational Poincaré duality space by means of a single cell attachment,
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$$\ell $$ ℓ -independence of the trace of local monodromy in a relative case (with an appendix by Qing Lu and Weizhe Zheng) manuscripta math. (IF 0.61) Pub Date : 2020-08-09 Hiroki Kato
For a family of varieties, we prove that the alternating sum of the traces of “local” monodromy acting on the \(\ell \)-adic étale cohomology groups of the generic fiber is an integer that is independent of \(\ell \). In the course of the proof, we also establish a result on fixed points.
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On singular moduli that are S -units manuscripta math. (IF 0.61) Pub Date : 2020-08-05 Francesco Campagna
Recently Yu. Bilu, P. Habegger and L. Kühne proved that no singular modulus can be a unit in the ring of algebraic integers. In this paper we study for which sets S of prime numbers there is no singular modulus that is an S-unit. Here we prove that if S is the set of all primes p congruent to 1 modulo 3, no singular modulus is an S-unit. We then give some remarks on the general case and we study the
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Trimmed sums of twists and the area Siegel–Veech constant manuscripta math. (IF 0.61) Pub Date : 2020-08-05 Vaibhav Gadre
We relate trimmed sums of twists in cylinders along a typical Teichmüller geodesic to the area Siegel–Veech constant.
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On a class of geodesic orbit spaces with abelian isotropy subgroup manuscripta math. (IF 0.61) Pub Date : 2020-08-05 Nikolaos Panagiotis Souris
Riemannian geodesic orbit spaces (G/H, g) are natural generalizations of symmetric spaces, defined by the property that their geodesics are orbits of one-parameter subgroups of G. We study the geodesic orbit spaces of the form (G/S, g), where G is a compact, connected, semisimple Lie group and S is abelian. We give a simple geometric characterization of those spaces, namely that they are naturally
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A note on Flenner’s extension theorem manuscripta math. (IF 0.61) Pub Date : 2020-08-04 Patrick Graf
We show that any p-form on the smooth locus of a normal complex space extends to a resolution of singularities, possibly with logarithmic poles, as long as \(p \le \mathrm {codim}_{X}({X}_{\mathrm {sg}}) - 2\). A stronger version of this result, allowing no poles at all, is originally due to Flenner. Our proof, however, is not only completely different, but also shorter and technically simpler. We
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Existence of solutions for the double phase variational problems without AR-condition manuscripta math. (IF 0.61) Pub Date : 2020-08-04 Jie Yang, Haibo Chen, Senli Liu
We consider the following double phase problem: $$\begin{aligned} -\mathrm {div}(|\nabla u|^{p-2}\nabla u+a(x)|\nabla u|^{q-2}\nabla u)+V(x)|u|^{\alpha -2}u=f(x,u),\quad \mathrm {in}\ \mathbb {R}^{N}, \end{aligned}$$ where \(N\ge 2,\) and \(\frac{q}{p}<1+\frac{1}{N}, a:\mathbb {R}^{N}\rightarrow [0,+\infty )~\mathrm {is~Lipschitz~continuous.}\) The Ambrosetti–Rabinowitz type condition, that is so-called
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Stratified $${{\mathcal {C}}}^p$$ C p -semialgebraic triviality manuscripta math. (IF 0.61) Pub Date : 2020-07-28 Anna Valette
We show that a stratified submersion between stratified semialgebraic sets is locally \({{\mathcal {C}}}^p\)-semialgebraically trivial outside the set of stratified generalized critical values.
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Existence of solution for a class of problem in whole $$\mathbb {R}^N$$ R N without the Ambrosetti–Rabinowitz condition manuscripta math. (IF 0.61) Pub Date : 2020-07-27 Claudianor O. Alves, Marco A. S. Souto
In this paper we study the existence of solution for a class of elliptic problem in whole \(\mathbb {R}^N\) without the well known Ambrosetti–Rabinowitz condition. Here, we do not assume any monotonicity condition on f(s)/s for \(s>0\).
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Rigidity theorem for holomorphic curves in a hyperquadric $$Q_n$$ Q n manuscripta math. (IF 0.61) Pub Date : 2020-07-26 Jie Fei, Jun Wang
In this paper, we prove that two linearly full holomorphic curves in a hyperquadric \(Q_n\), \(n\ge 2\), are congruent if their first fundamental forms and all kth covariant derivatives of the second fundamental forms, \(k=0,1,\ldots ,[\frac{|n-3|}{2}]\), are all the same.
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Codimension 2 cycles on Severi–Brauer varieties and decomposability manuscripta math. (IF 0.61) Pub Date : 2020-07-23 Eoin Mackall
In this text we show that one can generalize results showing that \(\mathrm {CH}^2(X)\), for various Severi–Brauer varieties X, is sometimes torsion free. In particular we show that for any pair of odd integers (n, m), with m dividing n and sharing the same prime factors, one can find a central simple k-algebra A of index n and exponent m that moreover has \(\mathrm {CH}^2(X)\) torsion free for \(X=\mathrm
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Diagram involutions and homogeneous Ricci-flat metrics manuscripta math. (IF 0.61) Pub Date : 2020-07-08 Diego Conti, Viviana del Barco, Federico A. Rossi
We introduce a combinatorial method to construct indefinite Ricci-flat metrics on nice nilpotent Lie groups. We prove that every nilpotent Lie group of dimension \(\le 6\), every nice nilpotent Lie group of dimension \(\le 7\) and every two-step nilpotent Lie group attached to a graph admits such a metric. We construct infinite families of Ricci-flat nilmanifolds associated to parabolic nilradicals
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A note on presentations of supersingular representations of $${\text {GL}}_2(F)$$ GL 2 ( F ) manuscripta math. (IF 0.61) Pub Date : 2020-07-03 Zhixiang Wu
We prove that any smooth irreducible supersingular representation with central character of \({\text {GL}}_2(F)\) is never of finite presentation when F is a finite field extension of \(\mathbb {Q}_p\) such that \(F\ne \mathbb {Q}_p\), extending a result of Schraen in (J Reine Angew Math (Crelle’s J) 2015(704):187–208, 2015) for quadratic extensions.
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Examples of smooth components of moduli spaces of stable sheaves manuscripta math. (IF 0.61) Pub Date : 2020-06-29 Fabian Reede, Ziyu Zhang
Let M be a projective fine moduli space of stable sheaves on a smooth projective variety X with a universal family \({\mathcal {E}}\). We prove that in four examples, \({\mathcal {E}}\) can be realized as a complete flat family of stable sheaves on M parametrized by X, which identifies X with a smooth connected component of some moduli space of stable sheaves on M.
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Homogeneous deformations of toric pairs manuscripta math. (IF 0.61) Pub Date : 2020-06-27 Andrea Petracci
We extend the Altmann–Mavlyutov construction of homogeneous deformations of affine toric varieties to the case of toric pairs \((X, \partial X)\), where X is an affine or projective toric variety and \(\partial X\) is its toric boundary. As an application, we generalise a result due to Ilten to the case of Fano toric pairs.
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Motivic double zeta values of odd weight manuscripta math. (IF 0.61) Pub Date : 2020-06-25 Jiangtao Li, Fei Liu
For odd \(N\ge 5\), we establish a short exact sequence about motivic double zeta values \(\zeta ^{\mathfrak {m}}(r,N-r)\) with \(r\ge 3\) odd, \(N-r\ge 2\). From this we classify all the relations among depth-graded motivic double zeta values \(\zeta ^{\mathfrak {m}}(r,N-r)\) with \(r\ge 3\) odd, \(N-r\ge 2\). As a corollary, we confirm a conjecture of Zagier on the rank of a matrix which concerns
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Theta lifts of generic representations for dual pairs $$(\text {Sp}_{2n}, \text {O}(V))$$(Sp2n,O(V)) manuscripta math. (IF 0.61) Pub Date : 2020-06-24 Petar Bakić
We determine the occurrence and explicitly describe the theta lifts on all levels of all the irreducible generic representations for the dual pair of groups \((\text {Sp}_{2n}, \text {O}(V))\) defined over a local nonarchimedean field \({\mathbb {F}}\) of characteristic 0. As a direct application of our results, we are able to produce a series of non-generic unitarizable representations of these groups
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On accumulation points of pseudo-effective thresholds manuscripta math. (IF 0.61) Pub Date : 2020-06-23 Jingjun Han, Zhan Li
We characterize a k-th accumulation point of pseudo-effective thresholds of n-dimensional varieties as certain invariant associates to a numerically trivial pair of an \((n-k)\)-dimensional variety. This characterization is applied towards Fujita’s log spectrum conjecture for large k.
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Bondal–Orlov fully faithfulness criterion for Deligne–Mumford stacks manuscripta math. (IF 0.61) Pub Date : 2020-06-20 Bronson Lim, Alexander Polishchuk
Suppose \(F:{\mathcal {D}}(X)\rightarrow {\mathcal {T}}\) is an exact functor from the bounded derived category of coherent sheaves on a smooth projective variety X to a triangulated category \({\mathcal {T}}\). If F possesses left and right adjoints, then the Bondal–Orlov criterion gives a simple way of determining if F is fully faithful. We prove a natural extension of this theorem to the case when
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Normal elements in the Iwasawa algebras of Chevalley groups manuscripta math. (IF 0.61) Pub Date : 2020-06-16 Dong Han, Jishnu Ray, Feng Wei
For a prime \(p>2\), let G be a semi-simple, simply connected, split Chevalley group over \({\mathbb {Z}}_p\), G(1) be the first congruence kernel of G and \(\Omega _{G(1)}\) be the mod-p Iwasawa algebra defined over the finite field \({\mathbb {F}}_p\). Ardakov et al. (Adv Math 218: 865–901, 2008) have shown that if p is a “nice prime ” (\(p \ge 5\) and \(p \not \mid (n+1)\) if the Lie algebra of
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Algebraic realization of actions of some finite groups manuscripta math. (IF 0.61) Pub Date : 2020-06-11 Karl Heinz Dovermann, Daniel J. Flores, Vincent Giambalvo
Let G be \(A_5\), \(A_4\), or a finite group with cyclic Sylow 2 subgroup. We show that every closed smooth G manifold M has a strongly algebraic model. This means, there exist a nonsingular real algebraic G variety X which is equivariantly diffeomorphic to M and all G vector bundles over X are strongly algebraic. Making use of improved blow-up techniques and the literature on equivariant bordism theory
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Dynamical Belyi maps and arboreal Galois groups manuscripta math. (IF 0.61) Pub Date : 2020-06-08 Irene I. Bouw, Özlem Ejder, Valentijn Karemaker
We consider a large class of so-called dynamical Belyi maps and study the Galois groups of iterates of such maps. From the combinatorial invariants of the maps, we construct a useful presentation of the geometric Galois groups as subgroups of automorphism groups of regular trees, in terms of iterated wreath products. Using results on the reduction of dynamical Belyi maps modulo certain primes, we obtain
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Descents of unipotent cuspidal representations of finite classical groups manuscripta math. (IF 0.61) Pub Date : 2020-06-08 Dongwen Liu, Zhicheng Wang
Inspired by the Gan–Gross–Prasad conjecture and the descent problem for classical groups, in this paper we study the descents of unipotent cuspidal representations of orthogonal and symplectic groups over finite fields.
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Solutions of the Laplacian flow and coflow of a locally conformal parallel $$\mathrm {G}_2$$G2 -structure manuscripta math. (IF 0.61) Pub Date : 2020-06-08 Victor Manero, Antonio Otal, Raquel Villacampa
We study the Laplacian flow of a \(\mathrm {G}_2\)-structure where this latter structure is claimed to be locally conformal parallel. The first examples of long time solutions of this flow with the locally conformal parallel condition are given. All of the solutions are ancient and Laplacian soliton of shrinking type. These examples are one-parameter families of locally conformal parallel \(\mathrm
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Entry loci and ranks manuscripta math. (IF 0.61) Pub Date : 2020-06-06 Edoardo Ballico, Emanuele Ventura
We study entry loci of varieties and their irreducibility from the perspective of X-ranks with respect to a projective variety X. These loci are the closures of the points that appear in an X-rank decomposition of a general point in the ambient space. We look at entry loci of low degree normal surfaces in \({\mathbb {P}}^4\) using Segre points of curves; the smooth case was classically studied by Franchetta
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A note on rigidity of Einstein four-manifolds with positive sectional curvature manuscripta math. (IF 0.61) Pub Date : 2020-06-06 Qing Cui, Linlin Sun
In this paper, we first prove a topological obstruction for a four-dimensional manifold carrying an Einstein metric. More precisely, assume (M, g) is a closed Einstein four-manifold with \(Ric=\rho g\). Denote by K the sectional curvature of M. If \(K\ge \delta \ge \frac{2\rho -\sqrt{5}\left|\rho \right|}{6}\) (or \(K\le \delta \le \frac{2\rho +\sqrt{5}}{6}\)) for some constant \(\delta \), then the
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Gradient estimates for nonlinear elliptic equations with first order terms manuscripta math. (IF 0.61) Pub Date : 2020-06-06 Stefano Buccheri
We study existence and Lorentz regularity of distributional solutions to elliptic equations with measurable coefficients and either a convection or a drift first order term. The presence of such a term makes the problem not coercive. The main tools are pointwise estimates of the rearrangements of both the solution and its gradient.
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Picard group of moduli of curves of low genus in positive characteristic manuscripta math. (IF 0.61) Pub Date : 2020-06-05 Andrea Di Lorenzo
We compute the Picard group of the moduli stack of smooth curves of genus g for \(3\le g\le 5\), using methods of equivariant intersection theory. We base our proof on the computation of some relations in the integral Chow ring of certain moduli stacks of smooth complete intersections. As a byproduct, we compute the cycle classes of some divisors on \(\mathcal {M}_g\).
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