IJPAM: Volume 21, No. 4 (2005)

RANK TWO VECTOR BUNDLES AND
SPECIAL RULED SURFACES

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 $F$ a rank two vector bundle on $X$. Is there $L\in \mbox{\rm Pic}(X)$ such that $h^1(X,F\otimes L) > 0$ and $F\otimes L$ is spanned ? Describe all such pairs $(F,L)$ (at least under certain assumptions on $X$ and $F$). Here we give complete results when $F$ is unstable and partial results when $F$ is stable and `` general '' in its stratum for the stratification given by the order of stability.

Received: May 6, 2005

AMS Subject Classification: 14H60, 14H50, 14J26

Key Words and Phrases: rank two vector bundles on curves, ruled surface, projective bundles, projective bundles on curves, unstable vector bundle

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