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Transactions of the American Mathematical Society

Published by the American Mathematical Society since 1900, Transactions of the American Mathematical Society is devoted to longer research articles in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.48.

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A categorical $\mathfrak {sl}_2$ action on some moduli spaces of sheaves
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by Nicolas Addington and Ryan Takahashi PDF
Trans. Amer. Math. Soc. 375 (2022), 8969-9005

Abstract:

We study certain sequences of moduli spaces of sheaves on K3 surfaces, building on work of Markman [J. Algebraic Geom. 10 (2001), pp. 623–694], Yoshioka [J. Reine Angew.Math. 515 (1999), pp. 97–123], and Nakajima [Convolution on homology groups of moduli spaces of sheaves on K3 surfaces, Contemp. Math., vol. 322, Amer. Math. Soc., Providence, RI, 2003, pp. 75–87]. We show that these sequences can be given the structure of a geometric categorical $\mathfrak {sl}_2$ action in the sense of Cautis, Kamnitzer, and Licata. As a corollary, we get an equivalence between derived categories of some moduli spaces that are birational via stratified Mukai flops.
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Additional Information
  • Nicolas Addington
  • Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222
  • MR Author ID: 939088
  • ORCID: 0000-0001-8346-3403
  • Email: adding@uoregon.edu
  • Ryan Takahashi
  • Affiliation: Department of Mathematics, University of Oregon, Eugene, Oregon 97403-1222
  • Email: rtakahas@uoregon.edu
  • Received by editor(s): December 20, 2021
  • Received by editor(s) in revised form: June 17, 2022, and June 27, 2022
  • Published electronically: September 23, 2022
  • Additional Notes: Both authors were partly supported by NSF grant no. DMS-1902213.
  • © Copyright 2022 by the authors
  • Journal: Trans. Amer. Math. Soc. 375 (2022), 8969-9005
  • MSC (2020): Primary 18N25, 14F08, 14J42, 17B10
  • DOI: https://doi.org/10.1090/tran/8779