A Sheaf Cohomology Restriction Formula on Toric Complete Intersections

Abstract

We prove a sheaf cohomology restriction (SCORE) formula for a class of vector bundles on complete intersections in toric varieties. The formula enables one to compute cohomology products on the complete intersection $X$ via computations on the ambient space $V$ and potentially compute certain quantum corrections to the classical sheaf cohomology ring. Schematically the formula reads $(s_1,...,s_r)_X = (s_1,...,s_r, g)_V$ with $g$ being an explicitly described quantity derived from the monad data of the bundle.