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

By A. Marian, D. Oprea. 2005

51 citations recorded by the source corpus.

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.

Subfields: Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/7bfc48f6bfbc31b65505cf23965537a1618ba7c8

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In Geometry and Topology

In Mathematical Physics

Citations in the corpus

The moduli space of stable quotients (2009, background): “The classes i are obtained from the cotangent lines on the domain (or, equivalently, pulled back from the Artin stack by A ).”
Stable quasimaps to GIT quotients (2011, background): “Specifically, (i) when X is a Grassmannian, the Quot schemes on C carry a perfect obstruction theory, see [34] and [9]; (ii) when X is a toric variety, the “toric compactifications” (or linear sigma models) of Givental and Morrison-Plesser also carry perfect obstruction theories; (iii) when X is the”
Relations in the tautological ring of the moduli space of curves (2013, background): “The analogue of Theorem 4 for the Quot scheme of a fixed nonsingular curve was observed in [12].”
Quot schemes of curves and surfaces: virtual classes, integrals, Euler characteristics (2019, methodology): “Many of the ideas developed here are related to collaborations with Alina Marian in [31, 32, 33, 34, 35, 36].”
Segre classes and Hilbert schemes of points (2015, background): “In comparison, the intersection theory of the Quot scheme of a curve may be pursued in a virtual sense for a fixed curve [15] or by letting the curve vary via the moduli space of stable quotients [16].”