3期

最新文章

• 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...
• 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...
• Algebraic approximation and the decomposition theorem for Kahler Calabi-Yau varieties AI翻译
  作者：Bakker, Benjamin; Guenancia, Henri; Lehn, Christian
  作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite Federale Toulouse Midi-Pyrenees (ComUE); Institut National des Sciences Appliquees de Toulouse; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Centre National de la Recherche Scientifique (CNRS); Technische Universitat Chemnitz
  摘要：We extend the decomposition theorem for numerically K-trivial varieties with log terminal singularities to the Kahler setting. Along the way we prove that all such varieties admit a strong locally trivial algebraic approximation, thus completing the numerically K-trivial case of a conjecture of Campana and Peternell.
• When any three solutions are independent AI翻译
  作者：Freitag, James; Jaoui, Remi; Moosa, Rahim
  作者单位：University of Illinois System; University of Illinois Chicago; University of Illinois Chicago Hospital; University of Freiburg; University of Waterloo
  摘要：Given an algebraic differential equation of order greater than one, it is shown that if there is any nontrivial algebraic relation amongst any number of distinct nonalgebraic solutions, along with their derivatives, then there is already such a relation between three solutions. In the autonomous situation when the equation is over constant parameters the assumption that the order be greater than one can be dropped, and a nontrivial algebraic relation exists already between two solutions. These...
• Quantum difference equation for Nakajima varieties AI翻译
  作者：Okounkov, A.; Smirnov, A.
  作者单位：Columbia University; HSE University (National Research University Higher School of Economics); University of North Carolina; University of North Carolina Chapel Hill; Russian Academy of Sciences; Steklov Mathematical Institute of the Russian Academy of Sciences
  摘要：For an arbitrary Nakajima quiver variety X, we construct an analog of the quantum dynamical Weyl group acting in its equivariant K-theory. The correct generalization of the Weyl group here is the fundamental groupoid of a certain periodic locally finite hyperplane arrangement in Pic(X) circle times C. We identify the lattice part of this groupoid with the operators of quantum difference equation for X. The cases of quivers of finite and affine type are illustrated by explicit examples.
• Distribution of values of quadratic forms at integral points AI翻译
  作者：Buterus, P.; Goetze, F.; Hille, T.; Margulis, G.
  作者单位：University of Gottingen; University of Bielefeld; Northwestern University; Yale University
  摘要：The number of lattice points in d-dimensional hyperbolic or elliptic shells {m : a < Q[m] < b}, which are restricted to rescaled and growing domains r Omega, is approximated by the volume. An effective error bound of order o(r(d-2)) for this approximation is proved based on Diophantine approximation properties of the quadratic form Q. These results allow to show effective variants of previous non-effective results in the quantitative Oppenheim problem and extend known effective results in dime...
• Diophantine approximation as Cosmic Censor for Kerr-AdS black holes AI翻译
  作者：Kehle, Christoph
  作者单位：University of Cambridge; Swiss Federal Institutes of Technology Domain; ETH Zurich
  摘要：The purpose of this paper is to show an unexpected connection between Diophantine approximation and the behavior of waves on black hole interiors with negative cosmological constant Lambda < 0 and explore the consequences of this for the Strong Cosmic Censorship conjecture in general relativity. We study linear scalar perturbations psi of Kerr-AdS solving square(g)psi - 2/3 Lambda psi = 0 with reflecting boundary conditions imposed at infinity. Understanding the behavior of psi at the Cauchy h...
• The canonical wall structure and intrinsic mirror symmetry AI翻译
  作者：Gross, Mark; Siebert, Bernd
  作者单位：University of Cambridge; University of Texas System; University of Texas Austin
  摘要：As announced in Gross and Siebert (in Algebraic geometry: Salt Lake City 2015, Proceedings of Symposia in Pure Mathematics, vol 97, no 2. AMS, Providence, pp 199-230, 2018) in 2016, we construct and prove consistency of the canonical wall structure. This construction starts with a log Calabi-Yau pair (X, D) and produces a wall structure, as defined in Gross et al. (Mem. Amer. Math. Soc. 278(1376), 1376, 1-103, 2022). Roughly put, the canonical wall structure is a data structure which encodes a...
• A homological approach to pseudoisotopy theory. I AI翻译
  作者：Krannich, Manuel
  作者单位：University of Cambridge
  摘要：We construct a zig-zag from the once delooped space of pseudoiso-topies of a closed 2n-disc to the once looped algebraic K -theory space of the integers and show that the maps involved are p-locally (2n - 4)-connected for n > 3 and large primes p. The proof uses the computation of the stable homology of the moduli space of high-dimensional handlebodies due to Botvinnik-Perlmutter and is independent of the classical approach to pseudoisotopy theory based on Igusa's stability theorem and work of...
• Characterising rectifiable metric spaces using tangent spaces AI翻译
  作者：Bate, David
  作者单位：University of Warwick
  摘要：We characterise rectifiable subsets of a complete metric space X in terms of local approximation, with respect to the Gromov-Hausdorff distance, by an n-dimensional Banach space. In fact, if E subset of X with H-n (E) < infinity and has positive lower density almost everywhere, we prove that it is sufficient that, at almost every point and each sufficiently small scale, E is approximated by a bi-Lipschitz image of Euclidean space. We also introduce a generalisation of Preiss's tangent measures...