IJPAM: Volume 19, No. 4 (2005)

STABLE COHERENT SYSTEMS ON INTEGRAL
PROJECTIVE VARIETIES: AN ASYMPTOTIC
EXISTENCE THEOREM

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


Abstract.Fix integers $k > n \ge 2$, an integral projective variety $X$, a rank $n$ vector bundle $E$ on $X$ and an ample line bundle $H$ on $X$. Here we prove the existence of an integer $t_0$ (depending only from $k, n, X, H,E$) such that for all integers $t \ge t_0$ a general $k$-dimensional linear subspace $V$ of $E(tH)$ spans $E(tH)$, the coherent system $(E,V)$ is $\alpha$-$H$-stable for every $\alpha \gg 0$ and the natural map $\bigwedge ^n(V) \to H^0(X,\mbox{\rm det}(E)(ntH))$ is injective.

Received: February 22, 2005

AMS Subject Classification: 14J60

Key Words and Phrases: coherent system, stable vector bundle, stable coherent system

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