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Journal of the American Mathematical Society
Journal of the American Mathematical Society
ISSN 1088-6834(online) ISSN 0894-0347(print)

 

Curve counting theories via stable objects I. DT/PT correspondence


Author: Yukinobu Toda
Journal: J. Amer. Math. Soc. 23 (2010), 1119-1157
MSC (2010): Primary 14D20; Secondary 18E30
Published electronically: April 16, 2010
MathSciNet review: 2669709
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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

DOI: http://dx.doi.org/10.1090/S0894-0347-10-00670-3
PII: S 0894-0347(10)00670-3
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.
Article copyright: © Copyright 2010 American Mathematical Society