Geometry & Topology 5 (2001) 287–318

DOI: 10.2140/gt.2001.5.287

arXiv: math.AG/0009025

Abstract

The Gopakumar–Vafa integrality conjecture is defined and studied for the local geometry of a super-rigid curve in a Calabi–Yau 3–fold. The integrality predicted in Gromov–Witten theory by the Gopakumar–Vafa BPS count is verified in a natural series of cases in this local geometry. The method involves Gromov–Witten computations, Möbius inversion, and a combinatorial analysis of the numbers of étale covers of a curve.

Keywords

Gromov–Witten invariants, BPS states, Calabi–Yau 3–folds

Mathematical Subject Classification

Primary: 14N35

Secondary: 81T30

References

Forward citations

Publication

Received: 13 October 2000
Revised: 8 June 2002
Accepted: 20 March 2001
Published: 24 March 2001
Corrected: 8 June 2002
Proposed: Robion Kirby
Seconded: Yasha Eliashberg, Simon Donaldson

Authors