Kyoto Journal of Mathematics

The banks of the cohomology river

David Eisenbud and Frank-Olaf Schreyer

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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.

Article information

Kyoto J. Math. Volume 53, Number 1 (2013), 131-144.

First available in Project Euclid: 25 March 2013

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Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

Primary: 14F05: Sheaves, derived categories of sheaves and related constructions [See also 14H60, 14J60, 18F20, 32Lxx, 46M20]
Secondary: 13D07: Homological functors on modules (Tor, Ext, etc.)


Eisenbud, David; Schreyer, Frank-Olaf. The banks of the cohomology river. Kyoto J. Math. 53 (2013), no. 1, 131--144. doi:10.1215/21562261-1966089.

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