Title: Enumerative invariants of Calabi-Yau threefolds with torsion
Abstract: In this talk, I focus on one example to illustrate a more general phenomenon. The double cover X of P^3 branched along the zero locus of a generic 8x8 matrix of linear forms is a singular Calabi-Yau threefold with 84 nodes. There are enumerative invariants of X associated with the B-model of a mirror Calabi-Yau, described in the A-model by considering all 2^{84} small resolutions X' of X, any one of which has a Z_2 torsion subgroup of H_2(X',Z). This set-up is related to topologically nontrivial B-fields, the Brauer group, and noncommutative resolutions. This talk is based on joint work in progress with Albrecht Klemm, Thorsten Schimannek, and Eric Sharpe.