Curve counting theories via stable objects I. DT/PT correspondence
arXiv:0902.4371
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.
43 pages, the Appendix is added, many mistakes are corrected
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Cited by in corpus (8)
- Refined, Motivic, and Quantum
- Motivic Donaldson-Thomas invariants and McKay correspondence
- Chamber Structure and Wallcrossing in The ADHM Theory of Curves I
- Hilbert schemes and stable pairs: GIT and derived category wall crossings
- On a computation of rank two Donaldson-Thomas invariants
- Counting invariants for the ADE McKay quivers
- Motivic Donaldson-Thomas invariants of the conifold and the refined topological vertex
- Wall-crossing formulas for framed objects