Duke Mathematical Journal

Virtual intersections on the Quot scheme and Vafa-Intriligator formulas

Alina Marian and Dragos Oprea

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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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Duke Math. J., Volume 136, Number 1 (2007), 81-113.

First available in Project Euclid: 4 December 2006

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Zentralblatt MATH identifier

Primary: 14N35: Gromov-Witten invariants, quantum cohomology, Gopakumar-Vafa invariants, Donaldson-Thomas invariants [See also 53D45]
Secondary: 14C17: Intersection theory, characteristic classes, intersection multiplicities [See also 13H15] 14H60: Vector bundles on curves and their moduli [See also 14D20, 14F05]


Marian, Alina; Oprea, Dragos. Virtual intersections on the $\mathrm{Quot}$ scheme and Vafa-Intriligator formulas. Duke Math. J. 136 (2007), no. 1, 81--113. doi:10.1215/S0012-7094-07-13613-5. https://projecteuclid.org/euclid.dmj/1165244880

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