BPS states of curves in Calabi--Yau 3--folds

Details BPS states of curves in Calabi--Yau 3--folds BPS states of curves in Calabi--Yau 3--folds

2000-09-03

arxiv.org/abs/math/0009025v3

Geom.Topol. 5 (2001) 287-318

Mathematics

Algebraic Geometry

Published by Geometry and Topology at http://www.maths.warwick.ac.uk/gt/GTVol5/paper9.abs.html Version 3 is GT version 2 and

Scientific paper

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.

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