Classical sheaf cohomology rings on Grassmannians

Abstract

Let the vector bundle $\mathcal{E}$ be a deformation of the tangent bundle over the Grassmannian $G(k,n)$. We compute the ring structure of sheaf cohomology valued in exterior powers of $\mathcal{E}$, also known as the polymology. This is the first part of a project studying the quantum sheaf cohomology of Grassmannians with deformations of the tangent bundle, a generalization of ordinary quantum cohomology rings of Grassmannians. A companion physics paper [arXiv:1512.08586] describes physical aspects of the theory, including a conjecture for the quantum sheaf cohomology ring, and numerous examples.

32 pages, comments welcome; v2: material on moduli added to section 4, and various typos corrected

References in corpus (4)

• The Revival of (0,2) Linear Sigma Models
• Recent Developments in (0,2) Mirror Symmetry
• Quantum sheaf cohomology on Grassmannians
• A Correlator Formula for Quantum Sheaf Cohomology

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• Quantum Sheaf Cohomology and Duality of Flag Manifolds
• (0,2) versions of exotic (2,2) GLSMs
• Quantum cohomology from mixed Higgs-Coulomb branches
• A survey of recent developments in GLSMs