IJPAM: Volume 20, No. 4 (2005)

COHERENT SYSTEMS WITH MANY ``SPREAD''
SECTIONS ON 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 genus $g$ hyperelliptic projective curve, $\alpha \in \mathbb {R}$, $\alpha \ge 0$, and integers $n \ge 2$, $k$ and $d$ such that $0 \le d \ne n(2g-2)$. Here we prove when there is an $\alpha$-stable coherent system $(E,V)$ on $X$ of type $(n,d,k)$ such that both $E$ and $\omega _X\otimes E^\ast$ are spanned if and only if $d$ is even and there is an $(\alpha /2)$-stable coherent system of type $(n,d/2,k)$ on ${\bf {P}}^1$.

Received: February 27, 2005

AMS Subject Classification: 14H60, 14H51

Key Words and Phrases: coherent system, vector bundles on curves,stable vector bundle, hyperelliptic curve

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 20
Issue: 4