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

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**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.## References

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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