## Kyoto Journal of Mathematics

### The banks of the cohomology river

#### Abstract

We give sharp bounds on the vanishing of the cohomology of a tensor product of vector bundles on $\mathbb {P}^{n}$ 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

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

Digital Object Identifier
doi:10.1215/21562261-1966089

Mathematical Reviews number (MathSciNet)
MR3049309

Zentralblatt MATH identifier
1271.14021

#### 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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