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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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Curve counting theories via stable objects I. DT/PT correspondence
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by Yukinobu Toda PDF
J. Amer. Math. Soc. 23 (2010), 1119-1157 Request permission

Abstract:

The Donaldson-Thomas invariant is a curve counting invariant on Calabi-Yau 3-folds via ideal sheaves. Another counting invariant via stable pairs is introduced by Pandharipande and Thomas, which counts pairs of curves and divisors on them. These two theories are conjecturally equivalent via generating functions, called DT/PT correspondence. In this paper, we show the Euler characteristic version of DT/PT correspondence, using the notion of weak stability conditions and the wall-crossing formula.
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Additional Information
  • Yukinobu Toda
  • Affiliation: Institute for the Physics and Mathematics of the Universe (IPMU), University of Tokyo, Kashiwano-ha 5-1-5, Kashiwa City, Chiba 277-8582, Japan
  • Email: toda-914@pj9.so-net.ne.jp
  • Received by editor(s): March 10, 2009
  • Received by editor(s) in revised form: March 8, 2010
  • Published electronically: April 16, 2010
  • Additional Notes: This work is supported by the World Premier International Research Center Initiative (WPI initiative), MEXT, Japan. This work is partially supported by EPSRC grant EP/F038461/1.
  • © Copyright 2010 American Mathematical Society
  • Journal: J. Amer. Math. Soc. 23 (2010), 1119-1157
  • MSC (2010): Primary 14D20; Secondary 18E30
  • DOI: https://doi.org/10.1090/S0894-0347-10-00670-3
  • MathSciNet review: 2669709