Abstract
We give sharp bounds on the vanishing of the cohomology of a tensor product of vector bundles on Pn 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.
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