Virtual intersections on the Quot-scheme and Vafa-Intriligator formulas

Details Virtual intersections on the Quot-scheme and Vafa-Intriligator formulas Virtual intersections on the Quot-scheme and Vafa-Intriligator formulas

2005-05-31

arxiv.org/abs/math/0505685v2

Mathematics

Algebraic Geometry

Scientific paper

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.

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