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Levi–Kähler reduction of CR structures, products of spheres, and toric geometry Math. Res. Lett. (IF 0.503) Pub Date : 2020-11-01 Vestislav Apostolov, David M. J. Calderbank, Paul Gauduchon, Eveline Legendre
We introduce a process, which we call Levi–Kähler reduction, for constructing Kähler manifolds and orbifolds from CR manifolds (of arbitrary codimension) with a transverse torus action. Most of the paper is devoted to the study of Levi–Kähler reductions of toric CR manifolds, and in particular, products of odd dimensional spheres. We obtain explicit descriptions and characterizations of the orbifolds
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On the radius of analyticity of solutions to semi-linear parabolic systems Math. Res. Lett. (IF 0.503) Pub Date : 2020-11-01 Jean-Yves Chemin, Isabelle Gallagher, Ping Zhang
We study the radius of analyticity $R(t)$ in space, of strong solutions to systems of scale-invariant semi-linear parabolic equations. It is well-known that near the initial time, $R(t)t^{-\frac{1}{2}}$ is bounded from below by a positive constant. In this paper we prove that $\displaystyle\liminf_{t\to 0} R(t)t^{-\frac{1}{2}}=\infty$, and assuming higher regularity for the initial data, we obtain
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The Chow cohomology of affine toric varieties Math. Res. Lett. (IF 0.503) Pub Date : 2020-11-01 Dan Edidin, Ryan Richey
We study the Fulton–Macpherson Chow cohomology of affine toric varieties. In particular, we prove that the Chow cohomology vanishes in positive degree. We prove an analogous result for the operational $K$‑theory defined by Anderson and Payne.
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Lifting $G$-irreducible but $\mathrm{GL}_n$-reducible Galois representations Math. Res. Lett. (IF 0.503) Pub Date : 2020-11-01 Najmuddin Fakhruddin, Chandrashekhar Khare, Stefan Patrikis
In recent work, the authors proved a general result on lifting $G$-irreducible odd Galois representations $\operatorname{Gal}(\overline{F}/F) \to G(\overline{\mathbb{F}}_\ell)$, with $F$ a totally real number field and $G$ a reductive group, to geometric $\ell$‑adic representations. In this note we take $G$ to be a classical group and construct many examples of $G$-irreducible representations to which
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Holomorphic families of Fatou–Bieberbach domains and applications to Oka manifolds Math. Res. Lett. (IF 0.503) Pub Date : 2020-11-01 Franc Forstnerič, Erlend Fornæss Wold
We construct holomorphically varying families of Fatou–Bieberbach domains with given centres in the complement of any compact polynomially convex subset $K$ of $\mathbb{C}^n$ for $n \gt 1$. This provides a simple proof of the recent result of $Y$. Kusakabe to the effect that the complement $\mathbb{C}^n \setminus K$ of any polynomially convex subset $K$ of $\mathbb{C}^n$ is an Oka manifold. The analogous
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Weight modules of quantum Weyl algebras Math. Res. Lett. (IF 0.503) Pub Date : 2020-11-01 Vyacheslav Futorny, Laurent Rigal, Andrea Solotar
We develop a general framework for studying relative weight representations for certain pairs consisting of an associative algebra and a commutative subalgebra. Using these tools we describe projective and simple weight modules for a common localisation of two quantum versions of Weyl algebras, one by Maltsiniotis and the other one by Akhavizadegan and Jordan, for generic values of the deformation
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Faithfulness of top local cohomology modules in domainss Math. Res. Lett. (IF 0.503) Pub Date : 2020-11-01 Melvin Hochster, Jack Jeffries
We study the conditions under which the highest nonvanishing local cohomology module of a domain $R$ with support in an ideal $I$ is faithful over $R$, i.e., which guarantee that $H^c_I (R)$ is faithful, where $c$ is the cohomological dimension of $I$. In particular, we prove that this is true for the case of positive prime characteristic when $c$ is the number of generators of $I$.
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The Dehn twist on a sum of two $K3$ surfaces Math. Res. Lett. (IF 0.503) Pub Date : 2020-11-01 P. B. Kronheimer, T. S. Mrowka
Ruberman gave the first examples of self-diffeomorphisms of four-manifolds that are isotopic to the identity in the topological category but not smoothly so. We give another example of this phenomenon, using the Dehn twist along a $3$-sphere in the connected sum of two $K3$ surfaces.
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Stability of tautological bundles on symmetric products of curves Math. Res. Lett. (IF 0.503) Pub Date : 2020-11-01 Andreas Krug
We prove that, if $C$ is a smooth projective curve over the complex numbers, and $E$ is a stable vector bundle on $C$ whose slope does not lie in the interval $[-1, n-1]$, then the associated tautological bundle $E^{[n]}$ on the symmetric product $C^{(n)}$ is again stable. Also, if $E$ is semi-stable and its slope does not lie in $[-1, n-1]$, then $E^{[n]}$ is semi-stable.
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Partial data inverse problems for semilinear elliptic equations with gradient nonlinearities Math. Res. Lett. (IF 0.503) Pub Date : 2020-11-01 Katya Krupchyk, Gunther Uhlmann
We show that the linear span of the set of scalar products of gradients of harmonic functions on a bounded smooth domain $\Omega \subset \mathbb{R}^n$ which vanish on a closed proper subset of the boundary is dense in $L^1 (\Omega)$. We apply this density result to solve some partial data inverse boundary problems for a class of semilinear elliptic PDE with quadratic gradient terms.
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Asymptotic behavior of the nonlinear Schrödinger equation on exterior domain Math. Res. Lett. (IF 0.503) Pub Date : 2020-11-01 Zhen-Hu Ning
We consider the following nonlinear Schrödinger equation on exterior domain:\[\begin{cases}iu_t+ \Delta_g u + ia(x)u-|u|^{p-1}u=0 & (x,t) \in \Omega \times (0,+ \infty), \\u {\big \vert}_{\Gamma}=0 & t \in (0,+ \infty), \\u (x,0) = u_0(x) & x \in \Omega,\end{cases}\] where $1\lt p \lt \frac{n+2}{n-2}$, $\Omega \subset \mathbb{R}^n (n \geq 3)$ is an exterior domain and $(\mathbb{R}^n , g)$ is a complete
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Generalizations of theorems of Nishino and Hartogs by the $L^2$ method Math. Res. Lett. (IF 0.503) Pub Date : 2020-11-01 Takeo Ohsawa
Three different generalizations will be given for Nishino’s rigidity theorem asserting the triviality of Stein families of $\mathbb{C}$ over the polydisc, in connection to generalizations of Hartogs’s theorem on the analyticity criterion for continuous functions.
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Nondiscreteness of $F$-thresholds Math. Res. Lett. (IF 0.503) Pub Date : 2020-11-01 Vijaylaxmi Trivedi
For every integer $g \gt 1$ and prime $p \gt 0$, we give an example of a standard graded domain $R$ (where Proj $R$ is a nonsingular projective curve of genus $g$ over an algebraically closed field of characteristic $p$), such that the set of $F$-thresholds of the irrelevant maximal ideal of $R$ is not discrete. This answers a question posed by Mustaţӑ–Takagi–Watanabe ([MTW], 2005). These examples
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On the four-vertex theorem for curves on locally convex surfacessurfaces Math. Res. Lett. (IF 0.503) Pub Date : 2020-09-01 Shibing Chen, Xu-Jia Wang, Bin Zhou
The classical four-vertex theorem describes a fundamental property of simple closed planar curves. It has been extended to space curves, namely a smooth, simple closed curve in $\mathbb{R}^3$ has at least four points with vanishing torsion if it lies on a convex surface. More recently, Ghomi [6] extended this property to curves lying on locally convex surfaces. In this paper we provide an alternative
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Springer correspondence, hyperelliptic curves, and cohomology of Fano varieties Math. Res. Lett. (IF 0.503) Pub Date : 2020-09-01 Tsao-Hsien Chen, Kari Vilonen, Ting Xue
In [CVX3] (T. H. Chen, K. Vilonen, and T. Xue, “Springer correspondence for the split symmetric pair in type A”, Compos. Math. 154 (2018), no. 11, 2403–2425), we have established a Springer theory for the symmetric pair $(\operatorname{SL}(N), \operatorname{SO}(N))$. In this setting we obtain representations of (the Tits extension) of the braid group rather than just Weyl group representations. These
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Complex Finsler vector bundles with positive Kobayashi curvature Math. Res. Lett. (IF 0.503) Pub Date : 2020-09-01 Huitao Feng, Kefeng Liu, Xueyuan Wan
In this short note, we prove that a complex Finsler vector bundle with positive Kobayashi curvature must be ample, which partially solves a problem of S. Kobayashi posed in 1975. As applications, a strongly pseudoconvex complex Finsler manifold with positive Kobayashi curvature must be biholomorphic to the complex projective space; we also show that all Schur polynomials are numerically positive for
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The Eisenbud–Green–Harris conjecture for defect two quadratic ideals Math. Res. Lett. (IF 0.503) Pub Date : 2020-09-01 Sema Güntürkün, Melvin Hochster
The Eisenbud–Green–Harris (EGH) conjecture states that a homogeneous ideal in a polynomial ring $K[x_1, \dotsc, x_n]$ over a field $K$ that contains a regular sequence $f_1, \dotsc , f_n$ with degrees $a_i, i =1, \dotsc , n$ has the same Hilbert function as a lex-plus-powers ideal containing the powers $x^{a_i}_i , i = 1, \dotsc , n$. In this paper, we discuss a case of the EGH conjecture for homogeneous
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Arithmetic surjectivity for zero-cycles Math. Res. Lett. (IF 0.503) Pub Date : 2020-09-01 Damián Gvirtz
Let $f : X \to Y$ be a proper, dominant morphism of smooth varieties over a number field $k$. When is it true that for almost all places $v$ of $k$, the fibre $X_P$ over any point $P \in Y (k_v)$ contains a zero-cycle of degree $1$? We develop a necessary and sufficient condition to answer this question. The proof extends logarithmic geometry tools that have recently been developed by Denef and Lo
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On weak Zariski decompositions and termination of flips Math. Res. Lett. (IF 0.503) Pub Date : 2020-09-01 Christopher Hacon, Joaquín Moraga
We prove that termination of lower dimensional flips for generalized $\operatorname{klt}$ pairs implies termination of flips for $\operatorname{log}$ canonical generalized pairs with a weak Zariski decomposition. Under the same hypothesis we prove that the existence of weak Zariski decompositions for pseudo-effective log canonical pairs implies the existence of weak Zariski decompositions for pseudo-effective
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Lagrangian antisurgery Math. Res. Lett. (IF 0.503) Pub Date : 2020-09-01 Luis Haug
We describe an operation which modifies a Lagrangian submanifold $L$ in a symplectic manifold $(M, \omega)$ such as to produce a new immersed Lagrangian submanifold $L^\prime$, which as a smooth manifold is obtained by surgery along a framed sphere in $L$. Intuitively, this can be described as collapsing an isotropic disc with boundary on $L$ to a point. The inverse operation generalizes classical
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Semiorthogonal decompositions of equivariant derived categories of invariant divisors Math. Res. Lett. (IF 0.503) Pub Date : 2020-09-01 Bronson Lim, Alexander Polishchuk
Given a smooth variety $X$ with an action of a finite group $G$, and a semiorthogonal decomposition of the derived category, $\mathcal{D}([X/G])$, of $G$-equivariant coherent sheaves on $X$ into subcategories equivalent to derived categories of smooth varieties, we construct a similar semiorthogonal decomposition for a smooth $G$-invariant divisor in $X$ (under certain technical assumptions). Combining
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One-relator groups with torsion are coherent Math. Res. Lett. (IF 0.503) Pub Date : 2020-09-01 Larsen Louder, Henry Wilton
We show that any one-relator group $G = F / {\langle \negthinspace \langle} w {\rangle \negthinspace \rangle}$ with torsion is coherent — i.e., that every finitely generated subgroup of $G$ is finitely presented — answering a 1974 question of Baumslag in this case.
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Period integrals in nonpositively curved manifolds Math. Res. Lett. (IF 0.503) Pub Date : 2020-09-01 Emmett L. Wyman
Let $M$ be a compact Riemannian manifold without boundary. We investigate the integrals of $L^2$-normalized Laplace eigenfunctions over closed submanifolds. General bounds for these quantities were obtained by Zelditch [23], and are sharp in the case where $M$ is the standard sphere. However, as with sup norms of eigenfunctions, there are many interesting settings where improvements can be made to
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Stability conditions and exceptional objects in triangulated categories Math. Res. Lett. (IF 0.503) Pub Date : 2020-07-01 Zihong Chen
The goal of this paper is to study the subspace of stability condition $\mathcal{E} \subset \operatorname{Stab}(X)$ associated to an exceptional collection $\mathcal{E}$ on a projective variety $X$. Following Macrì’s approach, we show a certain correspondence between the homotopy class of continuous loops in $\Sigma_\mathcal{E}$ and words of the braid group. In particular, we prove that in the case
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Applications of nonarchimedean developments to archimedean nonvanishing results for twisted $L$‑functions Math. Res. Lett. (IF 0.503) Pub Date : 2020-07-01 E. E. Eischen
We prove the nonvanishing of the twisted central critical values of a class of automorphic $L$‑functions for twists by all but finitely many unitary characters in particular infinite families. While this paper focuses on $L$‑functions associated to certain automorphic representations of unitary groups, it illustrates how decades-old non-archimedean methods from Iwasawa theory can be combined with the
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Minimal model program for log canonical threefolds in positive characteristic Math. Res. Lett. (IF 0.503) Pub Date : 2020-07-01 Kenta Hashizume, Yusuke Nakamura, Hiromu Tanaka
Given a three-dimensional projective log canonical pair over a perfect field of characteristic larger than five, there exists a minimal model program that terminates after finitely many steps.
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Upper semi-continuity of entropy in non-compact settings Math. Res. Lett. (IF 0.503) Pub Date : 2020-07-01 Godofredo Iommi, Mike Todd, Aníbal Velozo
We prove that the entropy map for countable Markov shifts of finite entropy is upper semi-continuous on the set of ergodic measures. Note that the phase space is non-compact. We also discuss the related problem of existence of measures of maximal entropy.
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Log canonical thresholds of Burniat surfaces with $K^2 = 6$ Math. Res. Lett. (IF 0.503) Pub Date : 2020-07-01 In-Kyun Kim, Yongjoo Shin
Let $S$ be a Burniat surface with $K^2_S = 6$. Then we show that $\operatorname{glct}(S, K_S) = \frac{1}{2}$ by showing that $\operatorname{glct}(S, 2K_S) = \operatorname{lct} (S, E) = \frac{1}{4}$ for some divisor $E \in \lvert 2K_S \rvert$. This implies that Tian’s conjecture (which fails in general) holds for the polarized pair $(S, 2K_S)$, since the corresponding graded algebra is generated by
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Mapping class group is generated by three involutions Math. Res. Lett. (IF 0.503) Pub Date : 2020-07-01 Mustafa Korkmaz
We prove that the mapping class group of a closed connected orientable surface of genus at least eight is generated by three involutions.
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On the $RO(G)$-graded coefficients of dihedral equivariant cohomology Math. Res. Lett. (IF 0.503) Pub Date : 2020-07-01 Igor Kriz, Yunze Lu
We completely calculate the $RO(G)$-graded coefficients of ordinary equivariant cohomology where $G$ is the dihedral group of order $2p$ for a prime $p \gt 2$ both with constant and Burnside ring coefficients. The authors first proved it for $p = 3$ and then the second author generalized it to arbitrary $p$. These are the first such calculations for a non-abelian group.
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On $L^1$ endpoint Kato–Ponce inequality Math. Res. Lett. (IF 0.503) Pub Date : 2020-07-01 Seungly Oh, Xinfeng Wu
We prove that the following endpoint Kato–Ponce inequality holds:\[{\lVert D^s (fg) \rVert}_{L^{\frac{q}{q+1}} (\mathbb{R}^n)}\lesssim{\lVert D^s f \rVert}_{L^1 (\mathbb{R}^n)}{\lVert g \rVert}_{L^q (\mathbb{R}^n)} \\+{\lVert f \rVert}_{L^1 (\mathbb{R}^n)}{\lVert D^s g \rVert}_{L^q (\mathbb{R}^n)}\; \textrm{,}\]for all $1 \leq q \leq \infty$, provided $s \gt n/q$ or $s \in 2 \mathbb{N}$. Endpoint estimates
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Chekanov’s dichotomy in contact topology Math. Res. Lett. (IF 0.503) Pub Date : 2020-07-01 Daniel Rosen, Jun Zhang
In this paper we study submanifolds of contact manifolds. The main submanifolds we are interested in are contact coisotropic submanifolds. They can be viewed as analogues to symplectic contact coisotropic submanifolds, and can be defined by the symplectic complement with respect to the symplectic structure $d \alpha \vert_\xi$, the restriction of $d \alpha$ on the contact hyperplane field $\xi$. Based
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Sphere theorems for submanifolds in Kähler manifold Math. Res. Lett. (IF 0.503) Pub Date : 2020-07-01 Jun Sun, Linlin Sun
In this paper, we prove some differentiable sphere theorems and topological sphere theorems for submanifolds in Kähler manifold, especially in complex space forms.
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Rational curves on elliptic K3 surfaces Math. Res. Lett. (IF 0.503) Pub Date : 2020-07-01 Salim Tayou
We prove that any non-isotrivial elliptic K3 surface over an algebraically closed field $k$ of arbitrary characteristic contains infinitely many rational curves. In the case when $\operatorname{char} (k) \neq 2, 3$, we prove this result for any elliptic K3 surface. When the characteristic of $k$ is zero, this result is due to the work of Bogomolov–Tschinkel and Hassett.
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Infinite-time singularity type of the Kähler–Ricci flow II Math. Res. Lett. (IF 0.503) Pub Date : 2020-07-01 Yashan Zhang
On a compact Kähler manifold with semi-ample canonical line bundle and Kodaira dimension one, we observe a relation between the infinite-time singularity type of the Kähler–Ricci flow and the characteristic indexes of singular fibers of the semi-ample fibration.
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From automorphisms of Riemann surfaces to smooth $4$-manifolds Math. Res. Lett. (IF 0.503) Pub Date : 2020-05-01 Ahmet Beyaz, Patrick Naylor, Sinem Onaran, B. Doug Park
Starting from a suitable set of self-diffeomorphisms of a closed Riemann surface, we present a general branched covering method to construct surface bundles over surfaces with positive signature. Armed with this method, we study the classification problem for both surface bundles with nonzero signature and closed simply connected smooth $\operatorname{spin} 4$-manifolds.
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WKB constructions in bidimensional magnetic wells Math. Res. Lett. (IF 0.503) Pub Date : 2020-05-01 Yannick Bonthonneau, Nicolas Raymond
This article establishes, in an analytic framework and in two dimensions, the first WKB constructions describing the eigenfunctions of the pure magnetic Laplacian with low energy when the magnetic field has a unique minimum that is positive and non-degenerate.
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Perelman’s $W$-functional on manifolds with conical singularities Math. Res. Lett. (IF 0.503) Pub Date : 2020-05-01 Xianzhe Dai, Changliang Wang
In this paper, we develop the theory of Perelman’s $W$-functional on manifolds with isolated conical singularities. In particular, we show that the infimum of $W$-functional over a certain weighted Sobolev space on manifolds with isolated conical singularities is finite, and the minimizer exists, if the scalar curvature satisfies certain condition near the singularities. We also obtain an asymptotic
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Lower bounds for estimates of the Schrödinger maximal function Math. Res. Lett. (IF 0.503) Pub Date : 2020-05-01 Xiumin Du, Jongchon Kim, Hong Wang, Ruixiang Zhang
We give new lower bounds for $L^p$ estimates of the Schrödinger maximal function by generalizing an example of Bourgain.
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Saddle hyperbolicity implies hyperbolicity for polynomial automorphisms of $\mathbb{C}^2$ Math. Res. Lett. (IF 0.503) Pub Date : 2020-05-01 Romain Dujardin
We prove that for a polynomial diffeomorphism of $\mathbb{C}^2$, uniform hyperbolicity on the set of saddle periodic points implies that saddle points are dense in the Julia set. In particular $f$ satisfies Smale’s Axiom A on $\mathbb{C}^2$.
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An action of $\mathfrak{gl}(1 \vert 1)$ on odd annular Khovanov homology Math. Res. Lett. (IF 0.503) Pub Date : 2020-05-01 J. Elisenda Grigsby, Stephan M. Wehrli
We define an annular version of odd Khovanov homology and prove that it carries an action of the Lie superalgebra $\mathfrak{gl}(1 \vert 1)$ which is preserved under annular Reidemeister moves.
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Quantitative upper bounds for Bergman kernels associated to smooth Kähler potentials Math. Res. Lett. (IF 0.503) Pub Date : 2020-05-01 Hamid Hezari, Hang Xu
We prove upper bounds for the Bergman kernels associated to tensor powers of a smooth positive line bundle in terms of the rate of growth of the Taylor coefficients of the Kähler potential. As applications, we obtain improved off-diagonal rate of decay for the classes of analytic, quasi-analytic, and more generally Gevrey potentials.
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Exact dynamical decay rate for the almost Mathieu operator Math. Res. Lett. (IF 0.503) Pub Date : 2020-05-01 Svetlana Jitomirskaya, Helge Krüger, Wencai Liu
We prove that the exponential decay rate in expectation is well defined and is equal to the Lyapunov exponent, for supercritical almost Mathieu operators with Diophantine frequencies.
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On the affine Schützenberger involution Math. Res. Lett. (IF 0.503) Pub Date : 2020-05-01 Dongkwan Kim
We consider an involution on the affine Weyl group of type $A$ induced from the nontrivial automorphism on the (finite) Dynkin diagram. We prove that the number of left cells fixed by this involution in each two-sided cell is given by a certain Green polynomial of type $A$ evaluated at $-1$.
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An example of liftings with different Hodge numbers Math. Res. Lett. (IF 0.503) Pub Date : 2020-05-01 Shizhang Li
In this paper, we exhibit an example of a smooth proper variety in positive characteristic possessing two liftings with different Hodge numbers.
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Inverse Galois problem for del Pezzo surfaces over finite fields Math. Res. Lett. (IF 0.503) Pub Date : 2020-05-01 Daniel Loughran, Andrey Trepalin
We completely solve the inverse Galois problem for del Pezzo surfaces of degree $2$ and $3$ over all finite fields.
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On Hawking mass and Bartnik mass of CMC surfaces Math. Res. Lett. (IF 0.503) Pub Date : 2020-05-01 Pengzi Miao, Yaohua Wang, Naqing Xie
Given a constant mean curvature surface that bounds a compact manifold with nonnegative scalar curvature, we obtain intrinsic conditions on the surface that guarantee the positivity of its Hawking mass. We also obtain estimates of the Bartnik mass of such surfaces, without assumptions on the integral of the squared mean curvature. If the ambient manifold has negative scalar curvature, our method also
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On completion of graded $D$-modules Math. Res. Lett. (IF 0.503) Pub Date : 2020-05-01 Nicholas Switala, Wenliang Zhang
Let $R = k[x_1, \dotsc , x_n]$ be a polynomial ring over a field $k$ of characteristic zero and $\widehat{R}$ be the formal power series ring $k[[x_1, \dotsc , x_n]]$. If $M$ is a $\mathcal{D}$-module over $R$, then $\widehat{R} \otimes_R M$ is naturally a $\mathcal{D}$-module over $\widehat{R}$. Hartshorne and Polini asked whether the natural maps $H^i_{\mathrm{dR}} (M) \to H^i_{\mathrm{dR}} (\widehat{R}
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Virtual Abelian varieties of $\mathrm{GL}_2$-type Math. Res. Lett. (IF 0.503) Pub Date : 2020-05-01 Chenyan Wu
This paper studies a class of Abelian varieties that are of $\mathrm{GL}_2$-type and with isogenous classes defined over a number field $k$. We treat the cases when their endomorphism algebras are either (1) a totally real field $K$ or (2) a totally indefinite quaternion algebra over a totally real field $K$. Among the isogenous class of such an Abelian variety, we identify one whose Galois conjugates
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