The Banks of the Cohomology River
arXiv:1109.4591 · doi:10.1215/21562261-1966089
Abstract
We give sharp bounds on the vanishing of the cohomology of a tensor product of vector bundles on the n-dimensional projective space in terms of the vanishing of the cohomology of the factors. For this purpose we introduce regularity indices generalizing the Castelnuovo-Mumford regularity. As an application we give a sufficient condition for a vector bundle to have an unobstructed deformation theory that depends only on the cohomology table of the bundle. We construct complete families of bundles with such cohomology tables.
16 pages