Mathematics – Algebraic Geometry
Scientific paper
2007-11-25
Jour. AMS. 23, 267-297, 2010.
Mathematics
Algebraic Geometry
Many results extended from irreducible curve case to reduced curve case. Typos fixed. Submitted version. 39 pages
Scientific paper
We define the BPS invariants of Gopakumar-Vafa in the case of irreducible curve classes on Calabi-Yau 3-folds. The main tools are the theory of stable pairs in the derived category and Behrend's constructible function approach to the virtual class. We prove that for irreducible classes the stable pairs generating function satisfies the strong BPS rationality conjectures. We define the contribution of each curve to the BPS invariants. A curve $C$ only contributes to the BPS invariants in genera lying between the geometric genus and arithmetic genus of $C$. Complete formulae are derived for nonsingular and nodal curves. A discussion of primitive classes on K3 surfaces from the point of view of stable pairs is given in the Appendix via calculations of Kawai-Yoshioka. A proof of the Yau-Zaslow formula for rational curve counts is obtained. A connection is made to the Katz-Klemm-Vafa formula for BPS counts in all genera.
Pandharipande Rahul
Thomas Raju P.
No associations
LandOfFree
Stable pairs and BPS invariants does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Stable pairs and BPS invariants, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Stable pairs and BPS invariants will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-512122