Degeneracy loci, virtual cycles and nested Hilbert schemes II
Algebraic Geometry
2020-10-07 v3 High Energy Physics - Theory
Representation Theory
Abstract
We express nested Hilbert schemes of points and curves on a smooth projective surface as "virtual resolutions" of degeneracy loci of maps of vector bundles on smooth ambient spaces. We show how to modify the resulting obstruction theories to produce the virtual cycles of Vafa-Witten theory and other sheaf-counting problems. The result is an effective way of calculating invariants (VW, SW, local PT and local DT) via Thom-Porteous-like Chern class formulae.
Keywords
Cite
@article{arxiv.1902.04128,
title = {Degeneracy loci, virtual cycles and nested Hilbert schemes II},
author = {Amin Gholampour and Richard P. Thomas},
journal= {arXiv preprint arXiv:1902.04128},
year = {2020}
}
Comments
42 pages. Two referees' corrections. To appear in Compositio