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Symplectic topology of K3 surfaces via mirror symmetry

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Original languageEnglish
Pages (from-to)875–915
Number of pages41
JournalJournal of the american mathematical society
Issue number3
Early online date9 Jun 2020
Publication statusE-pub ahead of print - 9 Jun 2020


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.

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