LAUSR

Abstract Let the vector bundle 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 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 [6] describes physical aspects of the theory, including a conjecture for the quantum sheaf cohomology ring, and numerous examples.