Classical sheaf cohomology rings on Grassmannians

Understand

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.