Gopakumar-Vafa BPS invariants, Hilbert schemes and quasimodular forms. I
Algebraic Geometry
2012-08-17 v1
Abstract
We prove a closed formula for leading Gopakumar- Vafa BPS invariants of local Calabi-Yau geometries given by the canonical line bundles of toric Fano surfaces. It shares some similar features with Goettsche-Yau-Zaslow formula: Connection with Hilbert schemes, connection with quasimodular forms, and quadratic property after suitable transformation. In Part I of this paper we will present the case of projective plane, more general cases will be presented in Part II.
Cite
@article{arxiv.1208.3270,
title = {Gopakumar-Vafa BPS invariants, Hilbert schemes and quasimodular forms. I},
author = {Shuai Guo and Jian Zhou},
journal= {arXiv preprint arXiv:1208.3270},
year = {2012}
}