2017/09/30 by Nick Sheridan, Ivan Smith · 1 citation
Mathematics · #math.SG
paper · pdf · doi:10.1090/jams/946
published as J. Amer. Math. Soc. 33 (2020), 875-915 · 40 pages; minor changes
arxiv created 2019/12/09 · arxiv updated 2020/11/03
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.