Annals of Mathematics

最新文章

• The index formula for the moduli of G-bundles on a curve AI翻译
  作者：Teleman, Constantin; Woodward, Christopher T.
  摘要：We prove the formulae conjectured by the first author for the index of K-theory classes over the moduli stack of algebraic G-bundles on a smooth projective curve. The formulae generalize E. Verlinde's for line bundles and have Witten's integrals over the moduli space of stable bundles as their large level limits. As an application, we prove the Newstead-Ramanan conjecture on the vanishing of high Chem classes of certain moduli spaces of semi-stable G-bundles.
• Finite groups of symplectic automorphisms of K3 surfaces in positive characteristic AI翻译
  作者：Dolgachev, Igor V.; Keum, JongHae
  摘要：We show that Mukai's classification of finite groups which may act symplectically on a complex K3 surface extends to positive characteristic p under assumptions that (i) the order of the group is coprime to p and (ii) either the surface or its quotient is not birationally isomorphic to a supersingular K3 surface with Artin invariant 1. In the case without assumption (ii) we classify all possible new groups which may appear. We prove that assumption (i) Oil the order of the group is always sati...
• On the decomposition of global conformal invariants, I AI翻译
  作者：Alexakis, Spyros
  摘要：This is the first of two papers where we address and partially confirm a conjecture of Deser and Schwimmer, originally postulated in high energy physics. The objects of study are scalar Riemannian quantities constructed out of the curvature and its covariant derivatives, whose integrals over compact manifolds are invariant under conformal changes of the underlying metric. Our main conclusion is that each such quantity that locally depends only on the curvature tensor (without covariant derivat...
• Polya-Schur master theorems for circular domains and their boundaries AI翻译
  作者：Borcea, Julius; Branden, Petter
  摘要：We characterize all linear operators on finite or infinite-dimensional polynomial spaces that preserve the property of having the zero set inside a prescribed region Omega subset of C for arbitrary closed circular domains Omega (i.e., images of the closed unit disk under a Mobius transformation) and their boundaries. This provides a natural framework for dealing with several long-standing fundamental problems, which we solve in a unified way. In particular, for Omega = R our results settle ope...
• A new upper bound for diagonal Ramsey numbers AI翻译
  作者：Conlon, David
  摘要：We prove a new upper bound for diagonal two-colour Ramsey numbers, showing that there exists a constant C such that r(k + 1, k + 1) <= k(-C log k/log log k) (2k k).
• Local connectivity of Julia sets for unicritical polynomials AI翻译
  作者：Kahn, Jeremy; Lyubich, Mikhail
  摘要：We prove that the Julia set J(f) of at most finitely renormalizable unicritical polynomial f : z bar right arrow z(d) + c with all periodic points repelling is locally connected. (For d = 2 it was proved by Yoccoz around 1990.) It follows from a priori bounds in a modified Principal Nest of puzzle pieces. The proof of a priori bounds makes use of new analytic tools developed in [KL09] that give control of moduli of annuli under maps of high degree.
• Inverse spectral problem for analytic domains, II: Z2-symmetric domains AI翻译
  作者：Zelditch, Steve
  摘要：This paper develops and implements a new algorithm for calculating wave trace invariants of a bounded plane domain around a periodic billiard orbit. The algorithm is based on a new expression for the localized wave trace as a special multiple oscillatory integral over the boundary, and on a Feynman diagrammatic analysis of the stationary phase expansion of the oscillatory integral. The algorithm is particularly effective for Euclidean plane domains possessing a Z(2) symmetry which reverses the...
• On the classification of isoparametric hypersurfaces with four distinct principal curvatures in spheres AI翻译
  作者：Immervoll, Stefan
  摘要：In this paper we give a new proof for the classification result in [3]. We show that isoparametric hypersurfaces with four distinct principal curvatures in spheres are of Clifford type provided that the multiplicities m(1), m(2) of the principal curvatures satisfy m(2) >= 2m(2) - 1. This inequality is satisfied for all but five possible pairs (m(1), m(2)) with m(1) <= m(2). Our proof implies that for (m(1), m(2)) not equal (1, 1) the Clifford system may be chosen in such a way that the associa...
• On the dimensions of conformal repellers. Randomness and parameter dependency AI翻译
  作者：Rugh, Hans Henrik
  摘要：Bowen's formula relates the Hausdorff dimension of a conformal repeller to the zero of a 'pressure' function. We present an elementary, self-contained proof to show that Bowen's formula holds for C-1 conformal repellers. We consider time-dependent conformal repellers obtained as invariant subsets for sequences of conformally expanding maps within a suitable class. We show that Bowen's formula generalizes to such a repeller and that if the sequence is picked at random then the Hausdorff dimensi...
• Toward a theory of rank one attractors AI翻译
  作者：Wang, Qiudong; Young, Lai-Sang