Emilio Dominguez
University of Maryland
Title
Emilio Dominguez
Abstract
Given a 3-term perfect complex E over a variety X and a nonnegative integer r, we define a virtual cycle over the r-th degeneracy loci of E. This is done by modifying the complex E after pulling it back to certain blow ups of X.
We apply this construction to complexes over the Picard variety and the Hilbert schemes of non-singular complex projective surfaces. We recover, reprove and strengthen some of the known results involving the reduced cycles and the virtual cycles of the Hilbert schemes related to the curve counting theory and Vafa-Witten theory, respectively. This talk is based on joint work with Amin Gholampour.
