-
作者：Miyaoka, Reiko
摘要：We give a correction of the proof of the homogeneity of isoparametric hypersurfaces with (g, m) = (6, 2).
-
作者：Charles, Francois
摘要：We investigate boundedness results for families of holomorphic symplectic varieties up to birational equivalence. We prove the analogue of Zarhin's trick for K3 surfaces by constructing big line bundles of low degree on certain moduli spaces of stable sheaves, and proving birational versions of Matsusaka's big theorem for holomorphic symplectic varieties. As a consequence of these results, we give a new geometric proof of the Tate conjecture for K3 surfaces over finite fields of characteristic...
-
作者：Ford, Kevin; Green, Ben; Konyagin, Sergei; Tao, Terence
摘要：Let G(X) denote the size of the largest gap between consecutive primes below X. Answering a question of Erdos, we show that G(X) >= f(X) log X log log X log log log log X/(log log log X)(2) where f(X) is a function tending to infinity with X. Our proof combines existing arguments with a random construction covering a set of primes by arithmetic progressions. As such, we rely on recent work on the existence and distribution of long arithmetic progressions consisting entirely of primes.
-
作者：De Philippis, Guido; Rindler, Filip
摘要：We establish a general structure theorem for the singular part of A-free Radon measures, where A is a linear PDE operator. By applying the theorem to suitably chosen differential operators A, we obtain a simple proof of Alberti's rank-one theorem and, for the first time, its extensions to functions of bounded deformation (BD). We also prove a structure theorem for the singular part of a finite family of normal currents. The latter result implies that the Rademacher theorem on the differentiabi...
-
作者：Filip, Simion
摘要：We prove that affine invariant manifolds in strata of flat surfaces are algebraic varieties. The result is deduced from a generalization of a theorem of Moller. Namely, we prove that the image of a certain twisted Abel-Jacobi map lands in the torsion of a factor of the Jacobians. This statement can be viewed as a splitting of certain mixed Hodge structures.
-
作者：Totaro, Burt
摘要：For a very general principally polarized complex abelian 3-fold, the Chow group of algebraic cycles is infinite modulo every prime number. In particular, this gives the first examples of complex varieties with infinite Chow groups modulo 2.
-
作者：Astorg, Matthieu; Buff, Xavier; Dujardin, Romain; Peters, Han; Raissy, Jasmin
摘要：We show that there exist polynomial endomorphisms of C-2, possessing a wandering Fatou component. These mappings are polynomial skew-products, and can be chosen to extend holomorphically of P-2(C). We also find real examples with wandering domains in R-2. The proof is based on parabolic implosion techniques, and is based on an original idea of M. Lyubich.
-
作者：Ellenberg, Jordan S.; Venkatesh, Akshay; Westerland, Craig
摘要：We prove a homological stabilization theorem for Hurwitz spaces: moduli spaces of branched covers of the complex projective line. This has the following arithmetic consequence: let l > 2 be prime and A a finite abelian l-group. Then there exists Q = Q(A) such that, for q greater than Q, a positive fraction of quadratic extensions of F-q(t) have the l-part of their class group isomorphic to A.
-
作者：Bourgain, Jean; Demeter, Ciprian; Guth, Larry
摘要：We prove the main conjecture in Vinogradov's Mean Value Theorem for degrees higher than three. This will be a consequence of a sharp decoupling inequality for curves.
-
作者：Bijakowski, Stephane; Pilloni, Vincent; Stroh, Benoit
