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arXiv · 1109.4591

The Banks of the Cohomology River

David Eisenbud·Frank-Olaf Schreyer
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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.

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David Eisenbud, Frank-Olaf Schreyer. 2011-09-21. The Banks of the Cohomology River. https://doi.org/10.1215/21562261-1966089

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