The Banks of the Cohomology River
Algebraic Geometry
2015-01-14 v1
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.
Keywords
Cite
@article{arxiv.1109.4591,
title = {The Banks of the Cohomology River},
author = {David Eisenbud and Frank-Olaf Schreyer},
journal= {arXiv preprint arXiv:1109.4591},
year = {2015}
}
Comments
16 pages