IJPAM: Volume 19, No. 4 (2005)

STABLE COHERENT SYSTEMS $(E,V)$ WITH
$\text{rank}(E) = \dim (V)$ ON PROJECTIVE VARIETIES

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


Abstract.Fix an integer $n \ge 2$, an integral projective variety $X$, a rank $n$ torsion free sheaf $E$ on $X$ and an ample line bundle $H$ on $X$. Here we prove the existence of an integer $t_0$ and a positive real number $\alpha _0$ (depending only from $X$, $E$ and $H$) such that for all integers $t \ge t_0$ there is an $n$-dimensional linear subspace $W \subseteq H^0(X,E(tH))$ such that the corent pair $(E(tH),W)$ is not $\alpha$-stable (with respect to the polarization $H$) for all real numbers $\alpha \ge \alpha _0$.

Received: February 22, 2005

AMS Subject Classification: 14J60, 14H60

Key Words and Phrases: coherent system, stable vectror bundle, unstable coherent system

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 19
Issue: 4