IJPAM: Volume 21, No. 4 (2005)

STABLE COHERENT SYSTEMS OF TYPE $(n,d,n+1)$
ON SMOOTH CURVES AND MAPS
TO PROJECTIVE SPACES

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 and connected projective curve and $(E,V)$ a spanned coherent system on $X$ of type $(n,d,n+1)$ such that $E$ has no trivial factor. Here we prove that the coherent system $(E,V)$ is $\alpha$-stable for all $\alpha \gg 0$. Furthermore, $(E,V)$ is $\alpha$-stable for all $\alpha \ge 0$ (resp. $\alpha > 0$) if and only if $E$ is stable (resp. semistable).

Received: May 6, 2005

AMS Subject Classification: 14H60

Key Words and Phrases: coherent system, stable coherent system on a curve, restricted tangent bundle, curves in projective spaces

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 21
Issue: 4