BPS invariants for resolutions of polyhedral singularities

Abstract

We study the BPS invariants of the preferred Calabi–Yau resolution of ADE polyhedral singularities C^3/G given by Nakamura's G-Hilbert schemes. Genus 0 BPS invariants are defined by means of the moduli space of torsion sheaves as proposed by Katz (J Differ Geom 79(2):185–195, 2008). We show that these invariants are equal to half the number of certain positive roots of an ADE root system associated to G. This is in agreement with the prediction given in Bryan and Gholampour (Invent Math, in press) via Gromov–Witten theory.

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