• Invent. math. (IF 2.986) Pub Date : 2021-01-04
Nero Budur, Robin van der Veer, Lei Wu, Peng Zhou

We prove a conjecture of the first author relating the Bernstein–Sato ideal of a finite collection of multivariate polynomials with cohomology support loci of rank one complex local systems. This generalizes a classical theorem of Malgrange and Kashiwara relating the b-function of a multivariate polynomial with the monodromy eigenvalues on the Milnor fibers cohomology.

更新日期：2021-01-05
• Invent. math. (IF 2.986) Pub Date : 2021-01-02
Matthew Hedden, Juanita Pinzón-Caicedo

We conjecture that satellite operations are either constant or have infinite rank in the concordance group. We reduce this to the difficult case of winding number zero satellites, and use SO(3) gauge theory to provide a general criterion sufficient for the image of a satellite operation to generate an infinite rank subgroup of the smooth concordance group $${\mathcal {C}}$$. Our criterion applies widely;

更新日期：2021-01-02
• Invent. math. (IF 2.986) Pub Date : 2021-01-01
Jian Ding, Jiaming Xia

We study the random field Ising model on $${\mathbb {Z}}^2$$ where the external field is given by i.i.d. Gaussian variables with mean zero and positive variance. We show that the effect of boundary conditions on the magnetization in a finite box decays exponentially in the distance to the boundary.

更新日期：2021-01-01
• Invent. math. (IF 2.986) Pub Date : 2021-01-01
Mathieu Lewin, Phan Thành Nam, Nicolas Rougerie

We provide a rigorous derivation of nonlinear Gibbs measures in two and three space dimensions, starting from many-body quantum systems in thermal equilibrium. More precisely, we prove that the grand-canonical Gibbs state of a large bosonic quantum system converges to the Gibbs measure of a nonlinear Schrödinger-type classical field theory, in terms of partition functions and reduced density matrices

更新日期：2021-01-01
• Invent. math. (IF 2.986) Pub Date : 2021-01-01
Xuemiao Chen, Song Sun

In this paper we give a complete algebro-geometric characterization of analytic tangent cones of admissible Hermitian–Yang–Mills connections over any reflexive sheaves.

更新日期：2021-01-01
• Invent. math. (IF 2.986) Pub Date : 2020-12-22
Jorge Castillejos, Samuel Evington, Aaron Tikuisis, Stuart White, Wilhelm Winter

We compute the nuclear dimension of separable, simple, unital, nuclear, $${\mathcal {Z}}$$-stable $$\mathrm {C}^*$$-algebras. This makes classification accessible from $${\mathcal {Z}}$$-stability and in particular brings large classes of $$\mathrm {C}^*$$-algebras associated to free and minimal actions of amenable groups on finite dimensional spaces within the scope of the Elliott classification programme

更新日期：2020-12-22
• Invent. math. (IF 2.986) Pub Date : 2020-11-30
Giulio Codogni, Zsolt Patakfalvi

The Chow–Mumford (CM) line bundle is a functorial line bundle on the base of any family of klt Fano varieties. It is conjectured that it yields a polarization on the moduli space of K-poly-stable klt Fano varieties. Proving ampleness of the CM line bundle boils down to showing semi-positivity/positivity statements about the CM-line bundle for families with K-semi-stable/K-polystable fibers. We prove

更新日期：2020-12-01
• Invent. math. (IF 2.986) Pub Date : 2020-11-26

We prove the holomorphic rigidity conjecture of Teichmüller space which loosely speaking states that the action of the mapping class group uniquely determines the Teichmüller space as a complex manifold. The method of proof is through harmonic maps. We prove that the singular set of a harmonic map from a smooth n-dimensional Riemannian domain to the Weil–Petersson completion $$\overline{\mathcal {T}}$$

更新日期：2020-11-27
• Invent. math. (IF 2.986) Pub Date : 2020-11-25
Giovanni Paolini, Mario Salvetti

We prove the $$K(\pi ,1)$$ conjecture for affine Artin groups: the complexified complement of an affine reflection arrangement is a classifying space. This is a long-standing problem, due to Arnol’d, Pham, and Thom. Our proof is based on recent advancements in the theory of dual Coxeter and Artin groups, as well as on several new results and constructions. In particular: we show that all affine noncrossing

更新日期：2020-11-25
• Invent. math. (IF 2.986) Pub Date : 2020-11-24
Hannah K. Larson

Let $$f:C \rightarrow \mathbb {P}^1$$ be a degree k genus g cover. The stratification of line bundles $$L \in {{\,\mathrm{Pic}\,}}^d(C)$$ by the splitting type of $$f_*L$$ is a refinement of the stratification by Brill–Noether loci $$W^r_d(C)$$. We prove that for general degree k covers, these strata are smooth of the expected dimension. In particular, this determines the dimensions of all irreducible

更新日期：2020-11-25
• Invent. math. (IF 2.986) Pub Date : 2020-11-20
Masaki Izumi, Hiroki Matui

This is the second part of our serial work on the classification of poly-$${\mathbb {Z}}$$ group actions on Kirchberg algebras. Based on technical results obtained in our previous work, we completely reduce the problem to the classification of continuous fields of Kirchberg algebras over the classifying spaces. As an application, we determine the number of cocycle conjugacy classes of outer $${\mathbb 更新日期：2020-11-21 • Invent. math. (IF 2.986) Pub Date : 2020-11-19 Mikołaj Frączyk We show that every sequence of torsion-free arithmetic congruence lattices in \(\mathrm{PGL}(2,{{{\mathbb {R}}}})$$ or $$\mathrm{PGL}(2,{{{\mathbb {C}}}})$$ satisfies a strong quantitative version of the limit multiplicity property. We deduce that for $$R>0$$ in certain range, growing linearly in the degree of the invariant trace field, the volume of the R-thin part of any congruence arithmetic hyperbolic

更新日期：2020-11-21
• Invent. math. (IF 2.986) Pub Date : 2020-11-14
Nick Sheridan, Ivan Smith

We prove Kontsevich’s homological mirror symmetry conjecture for certain mirror pairs arising from Batyrev–Borisov’s ‘dual reflexive Gorenstein cones’ construction. In particular we prove HMS for all Greene–Plesser mirror pairs (i.e., Calabi–Yau hypersurfaces in quotients of weighted projective spaces). We also prove it for certain mirror Calabi–Yau complete intersections arising from Borisov’s construction

更新日期：2020-11-21
• Invent. math. (IF 2.986) Pub Date : 2020-11-18
Michael Björklund, Zemer Kosloff, Stefaan Vaes

We determine the Krieger type of nonsingular Bernoulli actions $$G \curvearrowright \prod _{g \in G} (\{0,1\},\mu _g)$$. When G is abelian, we do this for arbitrary marginal measures $$\mu _g$$. We prove in particular that the action is never of type II$$_\infty$$ if G is abelian and not locally finite, answering Krengel’s question for $$G = {\mathbb {Z}}$$. When G is locally finite, we prove that

更新日期：2020-11-19
• Invent. math. (IF 2.986) Pub Date : 2020-11-18
Arman Darbinyan

We show the existence of finitely presented torsion-free groups with decidable word problem that cannot be embedded in any finitely generated group with decidable conjugacy problem. This answers a well-known question of Collins from the early 1970’s.

更新日期：2020-11-18
• Invent. math. (IF 2.986) Pub Date : 2020-11-12
Jason Bell, Efim Zelmanov

We determine the possible functions that can occur, up to asymptotic equivalence, as growth functions of semigroups, hereditary languages, and algebras.

更新日期：2020-11-13
• Invent. math. (IF 2.986) Pub Date : 2020-11-02
Tomás Ibarlucía

We show that all groups of a distinguished class of «large» topological groups, that of Roelcke precompact Polish groups, have Kazhdan’s Property (T). This answers a question of Tsankov and generalizes previous results by Bekka (for the infinite-dimensional unitary group) and by Evans and Tsankov (for oligomorphic groups). Further examples include the group $${{\,\mathrm{Aut}\,}}(\mu )$$ of measure-preserving

更新日期：2020-11-02
• Invent. math. (IF 2.986) Pub Date : 2020-10-30
William H. Meeks, Pablo Mira, Joaquín Pérez, Antonio Ros

We prove that two spheres of the same constant mean curvature in an arbitrary homogeneous three-manifold only differ by an ambient isometry, and we determine the values of the mean curvature for which such spheres exist. This gives a complete classification of immersed constant mean curvature spheres in three-dimensional homogeneous manifolds.

更新日期：2020-11-02
• Invent. math. (IF 2.986) Pub Date : 2020-10-23
Roman Bezrukavnikov, Ivan Losev

We compute the number of finite dimensional irreducible modules for the algebras quantizing Nakajima quiver varieties. We get a lower bound for all quivers and vectors of framing. We provide an exact count in the case when the quiver is of finite type or is of affine type and the framing is the coordinate vector at the extending vertex. The latter case precisely covers Etingof’s conjecture on the number

更新日期：2020-10-26
• Invent. math. (IF 2.986) Pub Date : 2020-10-22
Jonathan Hermon, Tom Hutchcroft

Let G be a connected, locally finite, transitive graph, and consider Bernoulli bond percolation on G. We prove that if G is nonamenable and $$p > p_c(G)$$ then there exists a positive constant $$c_p$$ such that \begin{aligned} \mathbf {P}_p(n \le |K| < \infty ) \le e^{-c_p n} \end{aligned} for every $$n\ge 1$$, where K is the cluster of the origin. We deduce the following two corollaries: 1. Every

更新日期：2020-10-26
• Invent. math. (IF 2.986) Pub Date : 2020-10-15
Moon-Jin Kang, Alexis F. Vasseur

We prove the uniqueness and stability of entropy shocks to the isentropic Euler systems among all vanishing viscosity limits of solutions to associated Navier–Stokes systems. To take into account the vanishing viscosity limit, we show a contraction property for any large perturbations of viscous shocks to the Navier–Stokes system. The contraction estimate does not depend on the strength of the viscosity

更新日期：2020-10-16
• Invent. math. (IF 2.986) Pub Date : 2020-10-14
Emmanuel Lecouturier

Let N and p be primes such that p divides the numerator of $$\frac{N-1}{12}$$. In this paper, we study the rank $$g_p$$ of the completion of the Hecke algebra acting on cuspidal modular forms of weight 2 and level $$\Gamma _0(N)$$ at the p-maximal Eisenstein ideal. We give in particular an explicit criterion to know if $$g_p \ge 3$$, thus answering partially a question of Mazur. In order to study $$g_p$$

更新日期：2020-10-14
• Invent. math. (IF 2.986) Pub Date : 2020-10-08
Paul Melvin, Hannah Schwartz

It is shown that any finite list of smooth closed simply-connected 4-manifolds homeomorphic to a given one X can be obtained by removing a single compact contractible submanifold (or cork) from X, and then regluing it by powers of a boundary diffeomorphism. We then use this result to ‘separate’ finite families of corks embedded in a fixed 4-manifold.

更新日期：2020-10-11
• Invent. math. (IF 2.986) Pub Date : 2020-10-06
Will Sawin

We prove a characteristic p analogue of a result of Massey which bounds the dimensions of the stalks of a perverse sheaf in terms of certain intersection multiplicities of the characteristic cycle of that sheaf. This uses the construction of the characteristic cycle of a perverse sheaf in characteristic p by Saito. We apply this to prove a conjecture of Shende and Tsimerman on the Betti numbers of

更新日期：2020-10-06
• Invent. math. (IF 2.986) Pub Date : 2020-10-04
Laurent Bartholdi, Dzmitry Dudko

We consider Thurston maps: branched self-coverings of the sphere with ultimately periodic critical points, and prove that the Thurston equivalence problem between them (continuous deformation of maps along with their critical orbits) is decidable. More precisely, we consider the action of mapping class groups, by pre- and post-composition, on branched coverings, and encode them algebraically as mapping

更新日期：2020-10-04
• Invent. math. (IF 2.986) Pub Date : 2020-10-01
Dietrich Häfner, Peter Hintz, András Vasy

We prove the linear stability of slowly rotating Kerr black holes as solutions of the Einstein vacuum equations: linearized perturbations of a Kerr metric decay at an inverse polynomial rate to a linearized Kerr metric plus a pure gauge term. We work in a natural wave map/DeTurck gauge and show that the pure gauge term can be taken to lie in a fixed 7-dimensional space with a simple geometric interpretation

更新日期：2020-10-02
• Invent. math. (IF 2.986) Pub Date : 2020-09-21
Robert Kurinczuk, Daniel Skodlerack, Shaun Stevens

For a classical group over a non-archimedean local field of odd residual characteristic p, we prove that two cuspidal types, defined over an algebraically closed field $${\mathbf {C}}$$ of characteristic different from p, intertwine if and only if they are conjugate. This completes work of the first and third authors who showed that every irreducible cuspidal $${\mathbf {C}}$$-representation of a classical

更新日期：2020-09-21
• Invent. math. (IF 2.986) Pub Date : 2020-09-17
Peter Petersen, Matthias Wink

We show that manifolds with $$\lceil \frac{n}{2} \rceil$$-positive curvature operators are rational homology spheres. This follows from a more general vanishing and estimation theorem for the pth Betti number of closed n-dimensional Riemannian manifolds with a lower bound on the average of the lowest $$n-p$$ eigenvalues of the curvature operator. This generalizes results due to D. Meyer, Gallot–Meyer

更新日期：2020-09-18
• Invent. math. (IF 2.986) Pub Date : 2020-09-10
Alessandro Pigati, Daniel Stern

Given a Hermitian line bundle $$L\rightarrow M$$ over a closed, oriented Riemannian manifold M, we study the asymptotic behavior, as $$\epsilon \rightarrow 0$$, of couples $$(u_\epsilon ,\nabla _\epsilon )$$ critical for the rescalings \begin{aligned} E_\epsilon (u,\nabla )=\int _M\Big (|\nabla u|^2+\epsilon ^2|F_\nabla |^2+\frac{1}{4\epsilon ^2}(1-|u|^2)^2\Big ) \end{aligned} of the self-dual

更新日期：2020-09-11
• Invent. math. (IF 2.986) Pub Date : 2020-09-10
Michael Kemeny

We introduce a relativization of the secant sheaves from Green and Lazarsfeld (A simple proof of Petri’s theorem on canonical curves, Geometry Today, 1984) and Ein and Lazarsfeld (Inventiones Math 190:603-646, 2012) and apply this construction to the study of syzygies of canonical curves. As a first application, we give a simpler proof of Voisin’s Theorem for general canonical curves. This completely

更新日期：2020-09-11
• Invent. math. (IF 2.986) Pub Date : 2020-08-29
Giuseppe Ancona

Let A be an abelian fourfold in characteristic p. We prove the standard conjecture of Hodge type for A, namely that the intersection product \begin{aligned} {\mathcal {Z}}^2_{\mathrm {num}}(A)_{{\mathbb {Q}}}\times {\mathcal {Z}}_{\mathrm {num}}^2(A)_{{\mathbb {Q}}} \longrightarrow {\mathbb {Q}}\end{aligned} is of signature $$(\rho _2 - \rho _1 +1; \rho _1 - 1)$$, with $$\rho _n=\dim {\mathcal 更新日期：2020-08-29 • Invent. math. (IF 2.986) Pub Date : 2020-08-26 Rhiannon Dougall, Richard Sharp The aim of this paper is to study growth properties of group extensions of hyperbolic dynamical systems, where we do not assume that the extension satisfies the symmetry conditions seen, for example, in the work of Stadlbauer on symmetric group extensions and of the authors on geodesic flows. Our main application is to growth rates of periodic orbits for covers of an Anosov flow: we reduce the problem 更新日期：2020-08-27 • Invent. math. (IF 2.986) Pub Date : 2020-08-05 Ewain Gwynne, Jason Miller We show that for each \(\gamma \in (0,2)$$, there is a unique metric (i.e., distance function) associated with $$\gamma$$-Liouville quantum gravity (LQG). More precisely, we show that for the whole-plane Gaussian free field (GFF) h, there is a unique random metric $$D_h$$ associated with the Riemannian metric tensor “$$e^{\gamma h} (dx^2 + dy^2)$$” on $${\mathbb {C}}$$ which is characterized by a

更新日期：2020-08-06
• Invent. math. (IF 2.986) Pub Date : 2020-07-28
Mikhail Karpukhin

In the present paper we use twistor theory in order to solve two problems related to harmonic maps from surfaces to Euclidean spheres $${\mathbb {S}}^n$$. First, we propose a new approach to isoperimetric eigenvalue inequalities based on energy index. Using this approach we show that for any positive k, the k-th non-zero eigenvalue of the Laplacian on the real projective plane endowed with a metric

更新日期：2020-07-28
• Invent. math. (IF 2.986) Pub Date : 2020-07-24
Nicolaus Heuer, Clara Löh

New constructions in group homology allow us to manufacture high-dimensional manifolds with controlled simplicial volume. We prove that for every dimension bigger than 3 the set of simplicial volumes of orientable closed connected manifolds is dense in $$\mathbb {R}_{\ge 0}$$. In dimension 4 we prove that every non-negative rational number is the simplicial volume of some orientable closed connected

更新日期：2020-07-24
• Invent. math. (IF 2.986) Pub Date : 2020-07-23
Jarod Alper, Harold Blum, Daniel Halpern-Leistner, Chenyang Xu

We prove that K-polystable log Fano pairs have reductive automorphism groups. In fact, we deduce this statement by establishing more general results concerning the S-completeness and $$\Theta$$-reductivity of the moduli of K-semistable log Fano pairs. Assuming the conjecture that K-semistability is an open condition, we prove that the Artin stack parametrizing K-semistable Fano varieties admits a

更新日期：2020-07-24
• Invent. math. (IF 2.986) Pub Date : 2020-07-23
Virginia Agostiniani, Mattia Fogagnolo, Lorenzo Mazzieri

In this paper we consider complete noncompact Riemannian manifolds (M, g) with nonnegative Ricci curvature and Euclidean volume growth, of dimension $$n \ge 3$$. For every bounded open subset $$\Omega \subset M$$ with smooth boundary, we prove that \begin{aligned} \int \limits _{\partial \Omega } \left| \frac{\mathrm{H}}{n-1}\right| ^{n-1} \!\!\!\!\!{\mathrm{d}}\sigma \,\,\ge \,\,{\mathrm{AVR}}(g)\

更新日期：2020-07-24
• Invent. math. (IF 2.986) Pub Date : 2020-07-20
Jonas Azzam, Steve Hofmann, José María Martell, Mihalis Mourgoglou, Xavier Tolsa

It is well-known that quantitative, scale invariant absolute continuity (more precisely, the weak-$$A_\infty$$ property) of harmonic measure with respect to surface measure, on the boundary of an open set $$\Omega \subset \mathbb {R}^{n+1}$$ with Ahlfors–David regular boundary, is equivalent to the solvability of the Dirichlet problem in $$\Omega$$, with data in $$L^p(\partial \Omega )$$ for some

更新日期：2020-07-21
• Invent. math. (IF 2.986) Pub Date : 2020-07-14
Chieh-Yu Chang, Yoshinori Mishiba

In the classical theory of multiple zeta values (MZV’s), Furusho proposed a conjecture asserting that the p-adic MZV’s satisfy the same $${\mathbb {Q}}$$-linear relations that their corresponding real-valued MZV counterparts satisfy. In this paper, we verify a stronger version of a function field analogue of Furusho’s conjecture in the sense that we are able to deal with all linear relations over an

更新日期：2020-07-14
• Invent. math. (IF 2.986) Pub Date : 2020-07-11
Thomas Budzinski, Baptiste Louf

We prove a conjecture of Benjamini and Curien stating that the local limits of uniform random triangulations whose genus is proportional to the number of faces are the planar stochastic hyperbolic triangulations (PSHT) defined in Curien (Probab Theory Relat Fields 165(3):509–540, 2016). The proof relies on a combinatorial argument and the Goulden–Jackson recurrence relation to obtain tightness, and

更新日期：2020-07-13
• Invent. math. (IF 2.986) Pub Date : 2020-07-06
Erez Lapid, Alberto Mínguez

In 1980 Zelevinsky introduced certain commuting varieties whose irreducible components classify complex, irreducible representations of the general linear group over a non-archimedean local field with a given supercuspidal support. We formulate geometric conditions for certain triples of such components and conjecture that these conditions are related to irreducibility of parabolic induction. The conditions

更新日期：2020-07-06
• Invent. math. (IF 2.986) Pub Date : 2020-06-26
Jon Chaika, Howard Masur

We show that the set of not uniquely ergodic d-IETs with permutation in the Rauzy class of the hyperelliptic permutation has Hausdorff dimension $$d-\frac{3}{2}$$ [in the $$(d-1)$$-dimension space of d-IETs] for $$d\ge 5$$. For $$d=4$$ this was shown by Athreya–Chaika and for $$d\in \{2,3\}$$ the set is known to have dimension $$d-2$$. This provides lower bounds on the Hausdorff dimension of non-weakly

更新日期：2020-06-26
• Invent. math. (IF 2.986) Pub Date : 2020-06-25
Alexander I. Efimov

We disprove two (unpublished) conjectures of Kontsevich which state generalized versions of categorical Hodge-to-de Rham degeneration for smooth and for proper DG categories (but not smooth and proper, in which case degeneration is proved by Kaledin (in: Algebra, geometry, and physics in the 21st century. Birkhäuser/Springer, Cham, pp 99–129, 2017). In particular, we show that there exists a minimal

更新日期：2020-06-26
• Invent. math. (IF 2.986) Pub Date : 2020-06-19
Hokuto Konno, Masaki Taniguchi

We show 10/8-type inequalities for some end-periodic 4-manifolds which have positive scalar curvature metrics on the ends. As an application, we construct a new family of closed 4-manifolds which do not admit positive scalar curvature metrics.

更新日期：2020-06-19
• Invent. math. (IF 2.986) Pub Date : 2020-06-17
Gilles Pisier

We construct the first example of a $$C^*$$-algebra A with the properties in the title. This gives a new example of non-nuclear A for which there is a unique $$C^*$$-norm on $$A \otimes A^{op}$$. This example is of particular interest in connection with the Connes–Kirchberg problem, which is equivalent to the question whether $$C^*({\mathbb {F}}_2)$$, which is known to have the LLP, also has the WEP

更新日期：2020-06-17
• Invent. math. (IF 2.986) Pub Date : 2020-06-15
Lawrence Ein, Wenbo Niu, Jinhyung Park

In recent years, the equations defining secant varieties and their syzygies have attracted considerable attention. The purpose of the present paper is to conduct a thorough study on secant varieties of curves by settling several conjectures and revealing interaction between singularities and syzygies. The main results assert that if the degree of the embedding line bundle of a nonsingular curve of

更新日期：2020-06-15
• Invent. math. (IF 2.986) Pub Date : 2020-06-11
Bo Liu, Xiaonan Ma

In this paper we obtain a localization formula in differential K-theory for $$S^1$$-actions. We establish a localization formula for equivariant $$\eta$$-invariants by combining this result with our extension of Goette’s result on the comparison of two types of equivariant $$\eta$$-invariants. An important step in our approach is to construct a pre-$$\lambda$$-ring structure in differential K-theory

更新日期：2020-06-11
• Invent. math. (IF 2.986) Pub Date : 2020-06-04
Miguel N. Walsh

We establish sharp estimates that adapt the polynomial method to arbitrary varieties. These include a partitioning theorem, estimates on polynomials vanishing on fixed sets and bounds for the number of connected components of real algebraic varieties. As a first application, we provide a general incidence estimate that is tight in its dependence on the size, degree and dimension of the varieties involved

更新日期：2020-06-04
• Invent. math. (IF 2.986) Pub Date : 2020-06-04
Dawei Chen, Martin Möller, Adrien Sauvaget, Don Zagier

We show that the Masur–Veech volumes and area Siegel–Veech constants can be obtained using intersection theory on strata of Abelian differentials with prescribed orders of zeros. As applications, we evaluate their large genus limits and compute the saddle connection Siegel–Veech constants for all strata. We also show that the same results hold for the spin and hyperelliptic components of the strata

更新日期：2020-06-04
• Invent. math. (IF 2.986) Pub Date : 2020-05-18
Brian Lawrence, Akshay Venkatesh

We give an alternative proof of Faltings’s theorem (Mordell’s conjecture): a curve of genus at least two over a number field has finitely many rational points. Our argument utilizes the set-up of Faltings’s original proof, but is in spirit closer to the methods of Chabauty and Kim: we replace the use of abelian varieties by a more detailed analysis of the variation of p-adic Galois representations

更新日期：2020-05-18
• Invent. math. (IF 2.986) Pub Date : 2020-04-30
Gwyn Bellamy, Alastair Craw

For a finite subgroup $$\Gamma \subset \mathrm {SL}(2,\mathbb {C})$$ and for $$n\ge 1$$, we use variation of GIT quotient for Nakajima quiver varieties to study the birational geometry of the Hilbert scheme of n points on the minimal resolution S of the Kleinian singularity $$\mathbb {C}^2/\Gamma$$. It is well known that $$X:={{\,\mathrm{{\mathrm {Hilb}}}\,}}^{[n]}(S)$$ is a projective, crepant resolution

更新日期：2020-04-30
• Invent. math. (IF 2.986) Pub Date : 2019-11-02
Adrian Nachman, Idan Regev, Daniel Tataru

We prove a Plancherel theorem for a nonlinear Fourier transform in two dimensions arising in the Inverse Scattering method for the defocusing Davey–Stewartson II equation. We then use it to prove global well-posedness and scattering in $$L^2$$ for defocusing DSII. This Plancherel theorem also implies global uniqueness in the inverse boundary value problem of Calderón in dimension 2, for conductivities

更新日期：2020-04-21
• Invent. math. (IF 2.986) Pub Date : 2019-11-27
Nguyen Viet Dang, Colin Guillarmou, Gabriel Rivière, Shu Shen

We study the twisted Ruelle zeta function $$\zeta _X(s)$$ for smooth Anosov vector fields X acting on flat vector bundles over smooth compact manifolds. In dimension 3, we prove the Fried conjecture, relating Reidemeister torsion and $$\zeta _X(0)$$. In higher dimensions, we show more generally that $$\zeta _X(0)$$ is locally constant with respect to the vector field X under a spectral condition. As

更新日期：2020-04-21
• Invent. math. (IF 2.986) Pub Date : 2019-11-04
Mircea Mustaţă, Mihnea Popa

We bound the generation level of the Hodge filtration on the localization along a hypersurface in terms of its minimal exponent. As a consequence, we obtain a local vanishing theorem for sheaves of forms with log poles. These results are extended to $${\mathbf {Q}}$$-divisors, and are derived from a result of independent interest on the generation level of the Hodge filtration on nearby and vanishing

更新日期：2020-04-21
• Invent. math. (IF 2.986) Pub Date : 2019-12-05
Amol Aggarwal

In this paper we consider the six-vertex model at ice point on an arbitrary three-bundle domain, which is a generalization of the domain-wall ice model on the square (or, equivalently, of a uniformly random alternating sign matrix). We show that this model exhibits the arctic boundary phenomenon, whose boundary is given by a union of explicit algebraic curves. This was originally predicted by Colomo

更新日期：2020-04-21
• Invent. math. (IF 2.986) Pub Date : 2019-12-05
Joachim Jelisiejew

We prove that the Hilbert scheme of points on a higher dimensional affine space is non-reduced and has components lying entirely in characteristic p for all primes p. In fact, we show that Vakil’s Murphy’s Law holds up to retraction for this scheme. Our main tool is a generalized version of the Białynicki-Birula decomposition.

更新日期：2020-04-21
• Invent. math. (IF 2.986) Pub Date : 2019-11-06
Alastair King, Yu Qiu

We introduce the cluster exchange groupoid associated to a non-degenerate quiver with potential, as an enhancement of the cluster exchange graph. In the case that arises from an (unpunctured) marked surface, where the exchange graph is modelled on the graph of triangulations of the marked surface, we show that the universal cover of this groupoid can be constructed using the covering graph of triangulations

更新日期：2020-04-21
• Invent. math. (IF 2.986) Pub Date : 2020-04-20
Peter Banks, Erik Panzer, Brent Pym

Kontsevich’s 1997 formula for the deformation quantization of Poisson brackets is a Feynman expansion involving volume integrals over moduli spaces of marked disks. We develop a systematic theory of integration on these moduli spaces via suitable algebras of polylogarithms, and use it to prove that Kontsevich’s integrals can be expressed as integer-linear combinations of multiple zeta values. Our proof

更新日期：2020-04-21
• Invent. math. (IF 2.986) Pub Date : 2020-04-16
Amine Marrakchi

We show that a factor M is full if and only if the $$C^*$$-algebra generated by its left and right regular representations contains the compact operators. We prove that the bicentralizer flow of a type $$\mathrm{III}_1$$ factor is always ergodic. As a consequence, for any type $$\mathrm{III}_1$$ factor M and any $$\lambda \in ]0,1]$$, there exists an irreducible AFD type $$\mathrm{III}_\lambda$$ subfactor

更新日期：2020-04-21
• Invent. math. (IF 2.986) Pub Date : 2020-04-15
Olivier Benoist, Olivier Wittenberg

We formulate the “real integral Hodge conjecture”, a version of the integral Hodge conjecture for real varieties, and raise the question of its validity for cycles of dimension 1 on uniruled and Calabi–Yau threefolds and on rationally connected varieties. We relate it to the problem of determining the image of the Borel–Haefliger cycle class map for 1-cycles, with the problem of deciding whether a

更新日期：2020-04-21
Contents have been reproduced by permission of the publishers.

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