Log Calabi-Yau surfaces and Jeffrey-Kirwan residues

Abstract

We use the mirror construction of Gross, Hacking and Keel in order to prove a version, for a class of log Calabi-Yau surfaces, of the general expectations appearing in physics, in the context of two-dimensional supersymmetric gauge theories, which relate Jeffrey-Kirwan residues of meromorphic forms to the B-model of Calabi-Yau manifolds. MSC2020: 14J33, 16G20, 81Q60.