Geometry & Topology

BPS states of curves in Calabi–Yau 3–folds

Jim Bryan and Rahul Pandharipande

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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

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

Received: 13 October 2000
Revised: 8 June 2002
Accepted: 20 March 2001
First available in Project Euclid: 21 December 2017

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Zentralblatt MATH identifier

Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
Secondary: 81T30: String and superstring theories; other extended objects (e.g., branes) [See also 83E30]

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


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.

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