Geodesic
Curve counting theories via stable objects I. DT/PT correspondence
Toda, Yukinobu1
1 Institute for the Physics and Mathematics of the Universe (IPMU), University of Tokyo, Kashiwano-ha 5-1-5, Kashiwa City, Chiba 277-8582, Japan
Journal of the American Mathematical Society, Tome 23 (2010) no. 4, pp. 1119-1157

Voir la notice de l'article provenant de la source American Mathematical Society

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.
DOI : 10.1090/S0894-0347-10-00670-3

Toda, Yukinobu 1

1 Institute for the Physics and Mathematics of the Universe (IPMU), University of Tokyo, Kashiwano-ha 5-1-5, Kashiwa City, Chiba 277-8582, Japan 
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Toda, Yukinobu. Curve counting theories via stable objects I. DT/PT correspondence. Journal of the American Mathematical Society, Tome 23 (2010) no. 4, pp. 1119-1157. doi: 10.1090/S0894-0347-10-00670-3

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