IJPAM: Volume 51, No. 1 (2009)

WEAKLY ACM VECTOR BUNDLES ON
RULED SURFACES AND THEIR BLOWING-UPS

E. Ballico
Department of Mathematics
University of Trento
380 50 Povo (Trento) - Via Sommarive, 14, ITALY
e-mail: ballico@science.unitn.it


Abstract.Let $Y$ be a geometrically ruled surface over a smooth projective curve. Let $X$ be obtained from $Y$ by finitely many blowing-ups. Here we study numerical properties of rank $r$ vector bundles on $Y$ (or $X$) which are weakly Cohen-Macaulay with respect to several polarizations and the boundness of their isomorphism classes.

Received: September 10, 2008

AMS Subject Classification: 14J60

Key Words and Phrases: ACM vector bundle, arithmetically Cohen-Macaulay vector bundle, ruled surface, blowing-up

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2009
Volume: 51
Issue: 1