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15 January 2007 Virtual intersections on the Quot scheme and Vafa-Intriligator formulas
Alina Marian, Dragos Oprea
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Duke Math. J. 136(1): 81-113 (15 January 2007). DOI: 10.1215/S0012-7094-07-13613-5

Abstract

We construct a virtual fundamental class on the Quot scheme parametrizing quotients of a trivial bundle on a smooth projective curve. We use the virtual localization formula to calculate virtual intersection numbers on Quot. As a consequence, we re-prove the Vafa-Intriligator formula; our answer is valid even when the Quot scheme is badly behaved. More intersections of Vafa-Intriligator type are computed by the same method. Finally, we present an application to the nonvanishing of the Pontryagin ring of the moduli space of bundles

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Alina Marian. Dragos Oprea. "Virtual intersections on the Quot scheme and Vafa-Intriligator formulas." Duke Math. J. 136 (1) 81 - 113, 15 January 2007. https://doi.org/10.1215/S0012-7094-07-13613-5

Information

Published: 15 January 2007
First available in Project Euclid: 4 December 2006

zbMATH: 1117.14055
MathSciNet: MR2271296
Digital Object Identifier: 10.1215/S0012-7094-07-13613-5

Subjects:
Primary: 14N35
Secondary: 14C17, 14H60

Rights: Copyright © 2007 Duke University Press

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Vol.136 • No. 1 • 15 January 2007
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