IJPAM: Volume 43, No. 3 (2008)


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 smooth genus $g$ curve. Fix integers $d \ge n >0$ such that $(n+1)d-ng -n(n+1)\ge 0$. Here we use a paper by L. Brambila-Paz to show the existence of a coherent system $(E,V)$ of type $(n,d,n+1)$ on $X$ with $E$ semistable, $V$ spanning a rank $n$ subsheaf of $E$ and which is $\alpha$-stable for all $\alpha > 0$.

Received: December 12, 2007

AMS Subject Classification: 14H60

Key Words and Phrases: vector bundle on curves, coherent systems on curves, Brill-Noether theory for vector bundles

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 43
Issue: 3