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作者：Adiprasito, Karim A.; Ziegler, Guenter M.
作者单位：Universite Paris Saclay; Free University of Berlin
摘要：We construct an infinite family of 4-polytopes whose realization spaces have dimension smaller or equal to 96. This in particular settles a problem going back to Legendre and Steinitz: whether and how the dimension of the realization space of a polytope is determined/bounded by its f-vector. From this, we derive an infinite family of combinatorially distinct 69-dimensional polytopes whose realization is unique up to projective transformation. This answers a problem posed by Perles and Shephard...
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作者：Bauer, Ingrid; Catanese, Fabrizio; Grunewald, Fritz
作者单位：University of Bayreuth
摘要：We use a canonical procedure associating to an algebraic number a first a hyperelliptic curve C-a, and then a triangle curve (D-a, G(a)) obtained through the normal closure of an associated Belyi function. In this way we show that the absolute Galois group Gal((Q) over bar /Q) acts faithfully on the set of isomorphism classes of marked triangle curves, and on the set of connected components of marked moduli spaces of surfaces isogenous to a higher product (these are the free quotients of a pro...
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作者：Puder, Doron
作者单位：Hebrew University of Jerusalem
摘要：We present a new approach to showing that random graphs are nearly optimal expanders. This approach is based on recent deep results in combinatorial group theory. It applies to both regular and irregular random graphs. Let be a random -regular graph on vertices, and let be the largest absolute value of a non-trivial eigenvalue of its adjacency matrix. It was conjectured by Alon (Combinatorica 6(2), 83-96, 1986) that a random -regular graph is almost Ramanujan, in the following sense: for every...
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作者：Voisin, Claire
作者单位：Centre National de la Recherche Scientifique (CNRS); Institut Polytechnique de Paris; Ecole Polytechnique; Institut Polytechnique de Paris; Ecole Polytechnique
摘要：We prove that the general quartic double solid with nodes does not admit a Chow theoretic decomposition of the diagonal, (or equivalently has a nontrivial universal group,) and the same holds if we replace in this statement Chow theoretic by cohomological. In particular, it is not stably rational. We also deduce that the general quartic double solid with seven nodes does not admit a universal codimension cycle parameterized by its intermediate Jacobian, and even does not admit a parametrizatio...
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作者：Putman, Andrew
作者单位：Rice University
摘要：The homology groups of many natural sequences of groups {G(n)}(n=1)(infinity) (e.g. general linear groups, mapping class groups, etc.) stabilize as n -> infinity. Indeed, there is a well-known machine for proving such results that goes back to early work of Quillen. Church and Farb discovered that many sequences of groups whose homology groups do not stabilize in the classical sense actually stabilize in some sense as representations. They called this phenomena representation stability. We pro...
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作者：Cheraghi, Davoud; Cheritat, Arnaud
作者单位：Imperial College London; Universite de Toulouse; Universite Toulouse III - Paul Sabatier; Universite de Bordeaux; Centre National de la Recherche Scientifique (CNRS); CNRS - National Institute for Mathematical Sciences (INSMI); Inria
摘要：Marmi, Moussa and Yoccoz conjectured that some error function , related to the approximation of the size of Siegel disks by some arithmetic function of the rotation number , is a Holder continuous function of with exponent . Using the renormalization invariant class of Inou and Shishikura, we prove this conjecture for the restriction of to a class of high type numbers.
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作者：Liu, Si-Qi; Ruan, Yongbin; Zhang, Youjin
作者单位：Tsinghua University; University of Michigan System; University of Michigan
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作者：Mann, Kathryn
作者单位：University of California System; University of California Berkeley
摘要：Let denote the fundamental group of a closed surface of genus . We show that every geometric representation of into the group of orientation-preserving homeomorphisms of the circle is rigid, meaning that its deformations form a single semi-conjugacy class. As a consequence, we give a new lower bound on the number of topological components of the space of representations of into . Precisely, for each nontrivial divisor of , there are at least components containing representations with Euler num...
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作者：Collins, Tristan C.; Tosatti, Valentino
作者单位：Harvard University; Northwestern University
摘要：We prove that the non-Kahler locus of a nef and big class on a compact complex manifold bimeromorphic to a Kahler manifold equals its null locus. In particular this gives an analytic proof of a theorem of Nakamaye and Ein-Lazarsfeld-Musta-Nakamaye-Popa. As an application, we show that finite time non-collapsing singularities of the Kahler-Ricci flow on compact Kahler manifolds always form along analytic subvarieties, thus answering a question of Feldman-Ilmanen-Knopf and Campana. We also exten...
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作者：Harada, Megumi; Kaveh, Kiumars
作者单位：McMaster University; Pennsylvania Commonwealth System of Higher Education (PCSHE); University of Pittsburgh
摘要：Let X be a smooth projective variety of dimension n over C equipped with a very ample Hermitian line bundle L. In the first part of the paper, we show that if there exists a toric degeneration of X satisfying some natural hypotheses (which are satisfied in many settings), then there exists a surjective continuous map from X to the special fiber X-0 which is a symplectomorphism on an open dense subset U. From this we are then able to construct a completely integrable system on X in the sense of...
