Symplectic topology of 𝐾3 surfaces via mirror symmetry

Sheridan, Nick; Smith, Ivan

doi:10.1090/jams/946

Symplectic topology of $K3$ surfaces via mirror symmetry
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by Nick Sheridan and Ivan Smith

J. Amer. Math. Soc. 33 (2020), 875-915

DOI: https://doi.org/10.1090/jams/946

Published electronically: June 9, 2020

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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.

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