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Journal of the American Mathematical Society

Published by the American Mathematical Society, the Journal of the American Mathematical Society (JAMS) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6834 (online) ISSN 0894-0347 (print)

The 2020 MCQ for Journal of the American Mathematical Society is 4.79.

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Symplectic topology of $K3$ surfaces via mirror symmetry
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by Nick Sheridan and Ivan Smith HTML | PDF
J. Amer. Math. Soc. 33 (2020), 875-915 Request permission

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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Additional 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