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

Toda, Yukinobu

doi:10.1090/S0894-0347-10-00670-3

Curve counting theories via stable objects I. DT/PT correspondence
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by Yukinobu Toda;

J. Amer. Math. Soc. 23 (2010), 1119-1157

DOI: https://doi.org/10.1090/S0894-0347-10-00670-3

Published electronically: April 16, 2010

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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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