IJPAM: Volume 26, No. 2 (2006)

LOW RANK INDECOMPOSABLE VECTOR BUNDLES
ON CERTAIN COMPACT COMPLEX MANIFOLDS

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Let $X$ be a compact and connected $n$-dimensional manifold ($n \ge 2$) such that $TX \cong \mathcal {O}_X^{\oplus (n-1)}
\oplus L$ for some $L\in \mbox{Pic}(X)$. Then one of the following cases occurs:

(a) for every integer $r \ge 2$ there is an indecomposable rank $r$ holomorphic vector bundle on $X$;

(b) $h^1(X,\mathcal {O}_X)=0$ and $h^0(X,TX) =n$;

(c) $h^0(X,TX) \ge n+1$, $h^1(X,\mathcal {O}_X)=0$ and $X$ is homogeneous.

Received: October 25, 2005

AMS Subject Classification: 32J18, 32L10

Key Words and Phrases: indecomposable vector bundle, holomorphic group action

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2006
Volume: 26
Issue: 2