BPS states of curves in Calabi--Yau 3--folds
arXiv:math/0009025 · doi:10.2140/gt.2001.5.287
Abstract
The Gopakumar-Vafa conjecture is defined and studied for the local geometry of a 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, Mobius inversion, and a combinatorial analysis of the numbers of etale covers of a curve.
Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper9.abs.html Version 3 is GT version 2 and has corrections to eq (2) on p 295, to 1st eq in Prop 2.1 and the tables on p 395