Physical aspects of quantum sheaf cohomology for deformations of tangent   bundles of toric varieties
  In this paper, we will outline computations of quantum sheaf cohomology for deformations of tangent bundles of toric varieties, for those deformations describable as deformations of toric Euler sequences. Quantum sheaf cohomology is a heterotic analogue of quantum cohomology, a quantum deformation of the classical product on sheaf cohomology groups, that computes nonperturbative corrections to analogues of (27*)^3 couplings in heterotic string computations. Previous computations have relied on either physics-based GLSM techniques or computation-intensive brute-force Cech cohomology techniques. This paper describes methods for greatly simplifying mathematical computations, and derives more general results than previously obtainable with GLSM techniques. We will outline recent results (rigorous proofs will appear elsewhere). 
R. Donagi, J. Guffin, S. Katz, E. Sharpe
hep-th math.AG