The intersection theory of the Grassmannian, known as Schubert calculus, is an important development in geometry, representation theory and combinatorics. The Quot scheme is a natural generalization of the Grassmannian. In particular, it provides a compactification of the space of morphisms from a smooth projective curve C to the Grassmannian. The intersection theory of the Quot scheme can be used to recover Vafa-Intriligator formulas, which calculate explicit expressions for the count of maps to the Grassmannian subject to incidence conditions with Schubert subvarieties.

The symplectic (or orthogonal) Grassmannian parameterizes isotropic subspaces of a vector space endowed with symplectic (or symmetric) bilinear form. I will present explicit formulas for certain intersection numbers of the symplectic and the orthogonal analogue of Quot schemes. Furthermore, I will compare these intersection numbers with the Gromovâ€“Ruanâ€“Witten invariants of the corresponding Grassmannians.

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Last updated: 09 Oct 2024