Virtual intersections on the Quot-scheme and Vafa-Intriligator formulas
Algebraic Geometry
2007-05-23 v2
Abstract
We construct a virtual fundamental class on the Quot scheme parametrizing quotients of a trivial bundle on a curve. We use the virtual localization formula to calculate virtual intersection numbers on Quot. As a consequence, we reprove the Vafa-Intriligator formula; our answer is valid even when the Quot scheme is badly behaved. More intersections are computed by the same method. Finally, we present an application to the non-vanishing of the Pontrjagin ring of the moduli space of bundles.
Keywords
Cite
@article{arxiv.math/0505685,
title = {Virtual intersections on the Quot-scheme and Vafa-Intriligator formulas},
author = {Alina Marian and Dragos Oprea},
journal= {arXiv preprint arXiv:math/0505685},
year = {2007}
}