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 âmirror quarticâ and âmirror double planeâ), equipped with certain KĂ€hler 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.References
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Bibliographic Information
- Nick Sheridan
- Affiliation: School of Mathematics, University of Edinburgh, Edinburgh EH9 3FD, United Kingdom
- MR Author ID: 962118
- ORCID: 0000-0002-6299-0682
- Ivan Smith
- Affiliation: Centre for Mathematical Sciences, University of Cambridge, Wilberforce Road, Cambridge CB3 0WB, United Kingdom
- MR Author ID: 650668
- Received by editor(s): December 3, 2017
- Received by editor(s) in revised form: July 11, 2019, and November 19, 2019
- Published electronically: June 9, 2020
- Additional Notes: The first author was supported in part by a Sloan Research Fellowship, a Royal Society University Research Fellowship, and by the National Science Foundation through Grant number DMS-1310604 and under agreement number DMS-1128155. The first author also acknowledges support from Princeton University and the Institute for Advanced Study.
The second author was supported in part by a Fellowship from EPSRC. - © Copyright 2020 American Mathematical Society
- Journal: J. Amer. Math. Soc. 33 (2020), 875-915
- MSC (2010): Primary 53D37; Secondary 53D12, 14F05, 14J28
- DOI: https://doi.org/10.1090/jams/946
- MathSciNet review: 4127905