IJPAM: Volume 51, No. 3 (2009)

BRILL-NOETHER THEORY FOR VECTOR BUNDLES
ON STABLE CURVES WITH TWO COMPONENTS,
A UNIQUE SINGULAR POINT AND BALANCED GENERA

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 stable curve with two irreducible components, $X = X_1\cup X_2$, such that $\sharp (X_1\cap X_2)=1$ and $p_a(X_1)=p_a(X_2)$. Here we construct several $\omega _X$-stable vector bundles on $X$ with many sections in terms of the gonality of $X_1$ and $X_2$.

Received: January 6, 2009

AMS Subject Classification: 14H60, 14H20, 14H51

Key Words and Phrases: torsion free sheaf, stable vector bundle, stable curve, reducible curve, Brill-Noether theory for vector bundles

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 51
Issue: 3