Inventiones mathematicae

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• Purely magnetic tunneling effect in two dimensions AI翻译
  作者：Bonnaillie-Noel, Virginie; Herau, Frederic; Raymond, Nicolas
  作者单位：Centre National de la Recherche Scientifique (CNRS); Universite PSL; Ecole Normale Superieure (ENS); Centre National de la Recherche Scientifique (CNRS); Nantes Universite; Universite d'Angers
  摘要：The magnetic Schrodinger operator, with Neumann boundary condition, on a smooth, bounded, and simply connected domain Omega of the Euclidean plane is considered in the semiclassical limit. When Omega has a symmetry axis, the semiclassical splitting of the first two eigenvalues is analyzed. The first explicit tunneling formula in a pure magnetic field is established. The analysis is based on a pseudo-differential reduction to the boundary and the proof of the first known optimal purely magnetic...
• G-uniform stability and Kahler-Einstein metrics on Fano varieties AI翻译
  作者：Li, Chi
  作者单位：Purdue University System; Purdue University; Rutgers University System; Rutgers University New Brunswick
  摘要：Let X be any Q-Fano variety and Aut(X)(0) be the identity component of the automorphism group of X. Let G be a connected reductive subgroup of Aut(X)(0) that contains a maximal torus of Aut(X)(0). We prove that X admits a Kahler-Einstein metric if and only if X is G-uniformly K-stable. This proves a version of Yau-Tian-Donaldson conjecture for arbitrary singular Fano varieties. A key new ingredient is a valuative criterion for G-uniform K-stability.
• Critical points of the Moser-Trudinger functional on closed surfaces AI翻译
  作者：De Marchis, Francesca; Malchiodi, Andrea; Martinazzi, Luca; Thizy, Pierre-Damien
  作者单位：Sapienza University Rome; Scuola Normale Superiore di Pisa; Centre National de la Recherche Scientifique (CNRS); Ecole Centrale de Lyon; Institut National des Sciences Appliquees de Lyon - INSA Lyon; Universite Claude Bernard Lyon 1; Universite Jean Monnet
  摘要：Given a closed Riemann surface (Sigma, g(0)) and any positive weight f is an element of C-infinity(Sigma), we use a minmax scheme together with compactness, quantization results and with sharp energy estimates to prove the existence of positive critical points of the functional I-p,I-beta(u) = 2 - p/2 (p parallel to u parallel to(2)(H1)/2 beta) p/2-p - in integral(Sigma)(e(up-) - 1) f d v(g0), for every p is an element of (1, 2) and beta > 0, or for p = 1 and beta is an element of (0, infinity...
• Very stable Higgs bundles, equivariant multiplicity and mirror symmetry AI翻译
  作者：Hausel, Tamas; Hitchin, Nigel
  作者单位：Institute of Science & Technology - Austria; University of Oxford
  摘要：We define and study the existence of very stable Higgs bundles on Riemann surfaces, how it implies a precise formula for the multiplicity of the very stable components of the global nilpotent cone and its relationship to mirror symmetry. Themain ingredients are the Bialynicki-Birula theory of C*-actions on semiprojective varieties, C* characters of indices of C*-equivariant coherent sheaves, Hecke transformation for Higgs bundles, relative Fourier-Mukai transform along the Hitchin fibration, h...
• Random integral matrices: universality of surjectivity and the cokernel AI翻译
  作者：Nguyen, Hoi H.; Wood, Melanie Matchett
  作者单位：University System of Ohio; Ohio State University; University of Wisconsin System; University of Wisconsin Madison
  摘要：For a random matrix of entries sampled independently from a fairly general distribution in Z we study the probability that the cokernel is isomorphic to a given finite abelian group, or when it is cyclic. This includes the probability that the linear map between the integer lattices given by the matrix is surjective. We show that these statistics are asymptotically universal (as the size of the matrix goes to infinity), given by precise formulas involving zeta values, and agree with distributi...
• Rigidity estimates for isometric and conformal maps from Sn-1 to Rn AI翻译
  作者：Luckhaus, Stephan; Zemas, Konstantinos
  作者单位：Leipzig University; University of Munster
  摘要：We investigate both linear and nonlinear stability aspects of rigid motions (resp. Mobius transformations) of Sn-1 among Sobolev maps from Sn-1 into R-n. Unlike similar in flavour results for maps defined on domains of R-n and mapping into R-n, not only an isometric (resp. conformal) deficit is necessary in this more flexible setting, but also a deficit measuring the distortion of Sn-1 under the maps in consideration. The latter is defined as an associated isoperimetric type of deficit. The fo...
• The Ruelle zeta function at zero for nearly hyperbolic 3-manifolds AI翻译
  作者：Cekic, Mihajlo; Delarue, Benjamin; Dyatlov, Semyon; Paternain, Gabriel P.
  作者单位：University of Zurich; Centre National de la Recherche Scientifique (CNRS); Universite Paris Saclay; University of Paderborn; Massachusetts Institute of Technology (MIT); University of Cambridge
  摘要：We show that for a generic conformal metric perturbation of a compact hyperbolic 3-manifold Sigma with Betti number b(1), the order of vanishing of the Ruelle zeta function at zero equals 4 - b(1), while in the hyperbolic case it is equal to 4 - 2b(1). This is in contrast to the 2-dimensional case where the order of vanishing is a topological invariant. The proof uses the microlocal approach to dynamical zeta functions, giving a geometric description of generalized Pollicott-Ruelle resonant di...
• Picard ranks of K3 surfaces over function fields and the Hecke orbit conjecture AI翻译
  作者：Maulik, Davesh; Shankar, Ananth N.; Tang, Yunqing
  作者单位：Massachusetts Institute of Technology (MIT); University of Wisconsin System; University of Wisconsin Madison; Princeton University
  摘要：Let X -> C be a non-isotrivial and generically ordinary family of K3 surfaces over a proper curve C in characteristic p >= 5. We prove that the geometric Picard rank jumps at infinitely many closed points of C. More generally, suppose that we are given the canonical model of a Shimura variety S of orthogonal type, associated to a lattice of signature (b, 2) that is self-dual at p. We prove that any generically ordinary proper curve C in S-(F) over barp intersects special divisors of S-(F) over...
• Lorentzian Calderon problem under curvature bounds AI翻译
  作者：Alexakis, Spyros; Feizmohammadi, Ali; Oksanen, Lauri
  作者单位：University of Toronto; University of London; University College London
  摘要：We introduce a method of solving inverse boundary value problems for wave equations on Lorentzian manifolds, and show that zeroth order coefficients can be recovered under certain curvature bounds. The set of Lorentzian metrics satisfying the curvature bounds has a non-empty interior in the sense of arbitrary, smooth perturbations of the metric, whereas all previous results on this problem impose conditions on the metric that force it to be real analytic with respect to a suitably defined time...
• The Galois action on symplectic K-theory AI翻译
  作者：Feng, Tony; Galatius, Soren; Venkatesh, Akshay
  作者单位：University of California System; University of California Berkeley; University of Copenhagen; Institute for Advanced Study - USA
  摘要：We study a symplectic variant of algebraic K-theory of the integers, which comes equipped with a canonical action of the absolute Galois group of Q. We compute this action explicitly. The representations we see are extensions of Tate twists Z(p)(2k - 1) by a trivial representation, and we characterize them by a universal property among such extensions. The key tool in the proof is the theory of complex multiplication for abelian varieties.