Localizing Virtual Cycles by Cosections
arXiv:1007.3085
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.
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