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作者：Schroeer, Stefan
摘要：We show that there is no family of Enriques surfaces over the ring of integers. This extends non-existence results of Minkowski for families of finite e ' tale schemes, of Tate and Ogg for families of elliptic curves, and of Fontaine and Abrashkin for families of abelian varieties and more general smooth proper schemes with certain restrictions on Hodge numbers. Our main idea is to study the local system of numerical classes of invertible sheaves. Among other things, our result also hinges on ...
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作者：Baldi, Gregorio; Ullmo, Emmanuel
摘要：Let Gamma subset of PU(1, n) be a lattice and Sr be the associated ball quotient. We prove that, if Sr contains infinitely many maximal complex totally geodesic subvarieties, then Gamma is arithmetic. We also prove an Ax-Schanuel Conjecture for Sr, similar to the one recently proven by Mok, Pila and Tsimerman. One of the main ingredients in the proofs is to realise Sr inside a period domain for polarised integral variations of Hodge structure and interpret totally geodesic subvarieties as unli...
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作者：Fish, Joel W.; Hofer, Helmut
摘要：We prove that for each Hamiltonian function H is an element of C infinity(R4, R) defined on the standard symplectic (R4, omega 0), for which M := H-1(0) is a non-empty compact regular energy level, the Hamiltonian flow on M is not minimal. That is, we prove there exists a closed invariant subset of the Hamiltonian flow in M that is neither null nor all of M. This answers the four-dimensional case of a more than twenty year old question of Michel Herman, part of which can be regarded as a speci...
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作者：Apisa, Paul; Wright, Alex
摘要：We classify GL(2, R) orbit closures of translation surfaces of rank at least half the genus plus 1.
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作者：Kang, Dong Yeap; Kelly, Tom; Kuhn, Daniela; Methuku, Abhishek; Osthus, Deryk
摘要：The Erdo ˝s-Faber-Lovasz conjecture (posed in 1972) states that the chromatic index of any linear hypergraph on n vertices is at most n. In this paper, we prove this conjecture for every large n. We also provide stability versions of this result, which confirm a prediction of Kahn.
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作者：Keel, Sean; Yu, Tony yue
摘要：Let U be an affine log Calabi-Yau variety containing an open algebraic torus. We show that the naive counts of rational curves in U uniquely determine a commutative associative algebra equipped with a compatible multilinear form. This proves a variant of the Frobenius structure conjecture by Gross-Hacking-Keel in mirror symmetry, and the spectrum of this algebra is supposed to give the hypothetical mirror family. Although the statement of our theorem involves only elementary algebraic geometry...
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作者：Khot, Subhash; Minzer, Dor; Safra, Muli
摘要：We prove that pseudorandom sets in Grassmann graph have near-perfect expansion. This completes the proof of the 2-to-2 Games Conjecture (albeit with imperfect completeness). Some implications of this new result are improved hardness results for Minimum Vertex Cover, improving on the work of Dinur and Safra [Ann. of Math. 162 (2005), 439-485], and new hardness gaps for Unique-Games. The Grassmann graph Grglobal contains induced subgraphs Gr(local) that are themselves isomorphic to Grassmann gra...
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作者：Fraczyk, Mikolaj; Gelander, Tsachik
摘要：We prove the following conjecture of Margulis. Let G be a higher rank simple Lie group, and let ? <= G be a discrete subgroup of infinite covol-ume. Then, the locally symmetric space ?\G/K admits injected balls of any radius. This can be considered as a geometric interpretation of the cel-ebrated Margulis normal subgroup theorem. However, it applies to general discrete subgroups not necessarily associated to lattices. Yet, the result is new even for subgroups of infinite index of lattices. We ...
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作者：Wendl, Chris
摘要：We develop new techniques to study regularity questions for moduli spaces of pseudoholomorphic curves that are multiply covered. Among the main results, we show that unbranched multiple covers of closed holomor-phic curves are generically regular, and simple index 0 curves in dimen-sions greater than four are generically super-rigid, implying, e.g., that the Gromov-Witten invariants of Calabi-Yau 3-folds reduce to sums of local in-variants for finite sets of embedded curves. We also establish ...
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作者：Chifan, Ionut; Ioana, Adrian; Osin, Denis; Sun, Bin
摘要：We introduce a new class of groups called wreath-like products. These groups are close relatives of the classical wreath products and arise naturally in the context of group theoretic Dehn filling. Unlike ordinary wreath products, many wreath-like products have Kazhdan's property (T). In this paper, we prove that any group G in a natural family of wreath-like products with property (T) is W*-superrigid: the group von Neumann algebra L(G) remembers the isomorphism class of G. This allows us to ...
