## Kyoto Journal of Mathematics

### Vanishing theorems for vector bundles generated by sections

#### Abstract

In this article we give a vanishing result for the cohomology groups $H^{p,q}(X,S^{\nu}E\otimes L)$, where $E$ is a vector bundle generated by sections and $L$ is an ample line bundle on a smooth projective variety $X$. We also give an application related to a result of Barth-Lefschetz type. A general nonvanishing result under the same hypothesis is given to prove the optimality of the vanishing result for some parameter values.

#### Article information

Source
Kyoto J. Math. Volume 50, Number 3 (2010), 469-479.

Dates
First available in Project Euclid: 11 August 2010

https://projecteuclid.org/euclid.kjm/1281531709

Digital Object Identifier
doi:10.1215/0023608X-2010-001

Mathematical Reviews number (MathSciNet)
MR2723859

Zentralblatt MATH identifier
1205.32018

Subjects
Primary: 32L20: Vanishing theorems

#### Citation

Laytimi, F.; Nagaraj, D. S. Vanishing theorems for vector bundles generated by sections. Kyoto J. Math. 50 (2010), no. 3, 469--479. doi:10.1215/0023608X-2010-001. https://projecteuclid.org/euclid.kjm/1281531709

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