Localizing Virtual Cycles by Cosections
Algebraic Geometry
2010-08-10 v2
Abstract
We show that a cosection of the obstruction sheaf of a perfect obstruction theory localizes the virtual cycle to the non-surjective locus of the cosection. We give algebraic constructions of localized Gysin maps and localized virtual cycles. Various applications of these constructions are discussed.
Cite
@article{arxiv.1007.3085,
title = {Localizing Virtual Cycles by Cosections},
author = {Young-Hoon Kiem and Jun Li},
journal= {arXiv preprint arXiv:1007.3085},
year = {2010}
}
Comments
This paper replaces the first half of our previous manuscript entitled "Gromov-Witten invariants of varieties with holomorphic 2-forms", arXiv:0707.2986, in which we used an analytic definition of localized Gysin maps and localized virtual cycles. Our new algebraic constructions make it possible to directly apply many developed techniques in algebraic geometry