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.
Citation
Jim Bryan. Rahul Pandharipande. "BPS states of curves in Calabi–Yau 3–folds." Geom. Topol. 5 (1) 287 - 318, 2001. https://doi.org/10.2140/gt.2001.5.287
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