Kyoto Journal of Mathematics

The banks of the cohomology river

David Eisenbud and 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 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

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

Dates
First available in Project Euclid: 25 March 2013

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1364218043

Digital Object Identifier
doi:10.1215/21562261-1966089

Mathematical Reviews number (MathSciNet)
MR3049309

Zentralblatt MATH identifier
1271.14021

Subjects
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.)

Citation

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. https://projecteuclid.org/euclid.kjm/1364218043


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References

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