IJPAM: Volume 50, No. 4 (2009)

A CONDITION FOR THE EXISTENCE OF
$H$-STABLE VECTOR BUNDLES ON REDUCIBLE CURVES

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: [email protected]


Abstract.Let $X$ be a nodal projective curve whose irreducible components are smooth. Here we give a necessary condition on a polarization $H$ for the existence of $H$-stable vector bundles on $X$ with fixed rank and multidegree. If the dual graph of $X$ is a tree we look at vector bundles on $X$ with rank $r$ and $k<r$ sections whose evaluation at every $P\in X$ are linearly independent.

Received: December 20, 2008

AMS Subject Classification: 14H60, 14H20

Key Words and Phrases: torsion free sheaf, reducible curve, stable vector bundle

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 50
Issue: 4