Geometry & Topology, Vol. 5 (2001) Paper no. 9, pages 287-318.

BPS states of curves in Calabi-Yau 3-folds

Jim Bryan, Rahul Pandharipande

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.

Keywords. Gromov-Witten invariants, BPS states, Calabi-Yau 3-folds

AMS subject classification. Primary: 14N35. Secondary: 81T30.

DOI: 10.2140/gt.2001.5.287

E-print: arXiv:math.AG/0009025

Submitted to GT on 13 October 2000. Paper accepted 20 March 2001. Paper published 24 March 2001.

GT version 2 published 8 June 2002:
Corrections to equation (2) page 295, to the first equation in Prop 2.1 and to the tables on page 318.

GT version 2:

Notes on file formats

GT version 1:

Jim Bryan, Rahul Pandharipande
Department of Mathematics,Tulane University
6823 St. Charles Ave, New Orleans, LA 70118, USA
Department of Mathematics, California Institute of Technology
Pasadena, CA 91125, USA

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