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arXiv:1709.09439math.SG

Symplectic topology of K3 surfaces via mirror symmetry

Nick Sheridan, Ivan Smith

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Abstract

We study the symplectic topology of certain K3 surfaces (including the "mirror quartic" and "mirror double plane"), equipped with certain Kähler 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.

arXiv comments
40 pages; minor changes
Journal reference
J. Amer. Math. Soc. 33 (2020), 875-915
DOI
doi:10.1090/jams/946
Subjects
math.SGSymplectic Geometry

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  1. Show HN: Arxiv Vanity – Read academic papers from Arxiv as responsive web pages 1 comment

    • Unfortunately it's failing on first things I tried with a not-so-helpful error message: https://www.arxiv-vanity.com/papers/1608.04012/ https://www.arxiv-vanity.com/papers/0903.3065/ Also a lot of MathJax failures (maybe Latex variables names?)…

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