IJPAM: Volume 21, No. 2 (2005)

SHORT EXACT SEQUENCES OF POLYSTABLE
AND SPLIT VECTOR BUNDLES ON ELLIPTIC
AND BIELLIPTIC CURVES

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 either an elliptic curve or a bielliptic curve. Here we prove the existence (for suitable numerical invariants) of exact sequences

\begin{displaymath}0 \to S \to E \to Q \to 0\end{displaymath}

of vector bundles on $X$ such that $S$ is a direct sum of line bundles, while $E$ and $Q$ are polystable. If $X$ is elliptic, we also consider the case $E \cong \mathcal {O}_X^{\oplus e}$ (i.e. the pull-back of the universal exact sequence on a suitable Grassmannian).

Received: April 22, 2005

AMS Subject Classification: 14H60

Key Words and Phrases: vector bundles on curves, stable vector bundles, bielliptic curve, elliptic curve, polystable vector bundle

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2005
Volume: 21
Issue: 2