基于镜像对称的$K3$曲面的辛拓扑

IF 3.5 1区数学 Q1 MATHEMATICS

Journal of the American Mathematical Society Pub Date : 2017-09-27 DOI:10.1090/JAMS/946

Nick Sheridan, I. Smith

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引用次数: 18

摘要

我们研究了具有某些Kahler形式的某些K3曲面（包括“镜像四次曲面”和“镜像双平面”）的辛拓扑。特别地，我们证明了辛Torelli群可以无限生成，并导出了拉格朗日环面上的新约束。通过同源镜像对称的关键输入是Bayer和Bridgeland在Picard秩为1的代数K3曲面的导出范畴的自等价群上的结果。

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Symplectic topology of $K3$ surfaces via mirror symmetry

We study the symplectic topology of certain K3 surfaces (including the "mirror quartic" and "mirror double plane"), equipped with certain Kahler forms. In particular, we prove that the symplectic Torelli group may be infinitely generated, and derive new constraints on Lagrangian tori. The key input, via homological mirror symmetry, is a result of Bayer and Bridgeland on the autoequivalence group of the derived category of an algebraic K3 surface of Picard rank one.

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来源期刊

Journal of the American Mathematical Society 数学-数学

CiteScore

7.60

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： All articles submitted to this journal are peer-reviewed. The AMS has a single blind peer-review process in which the reviewers know who the authors of the manuscript are, but the authors do not have access to the information on who the peer reviewers are. This journal is devoted to research articles of the highest quality in all areas of pure and applied mathematics.