Genus Zero BPS Invariants for Local P-1

Abstract

We study the equivariant version of the genus zero BPS invariants of the total space of a rank 2 bundle on P-1 whose determinant is O-P1(-2). We define the equivariant genus zero BPS invariants by the residue integrals on the moduli space of stable sheaves of dimension one as proposed by Katz [11]. We compute these invariants for low degrees by counting the torus fixed stable sheaves. The results agree with the prediction in local Gromov-Witten theory studied in [3].