## Geometry & Topology

### BPS states of curves in Calabi–Yau 3–folds

#### 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.

#### Article information

Source
Geom. Topol., Volume 5, Number 1 (2001), 287-318.

Dates
Revised: 8 June 2002
Accepted: 20 March 2001
First available in Project Euclid: 21 December 2017

https://projecteuclid.org/euclid.gt/1513882990

Digital Object Identifier
doi:10.2140/gt.2001.5.287

Mathematical Reviews number (MathSciNet)
MR1825668

Zentralblatt MATH identifier
1063.14068

#### Citation

Bryan, Jim; Pandharipande, Rahul. BPS states of curves in Calabi–Yau 3–folds. Geom. Topol. 5 (2001), no. 1, 287--318. doi:10.2140/gt.2001.5.287. https://projecteuclid.org/euclid.gt/1513882990

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