IJPAM: Volume 51, No. 3 (2009)

ON THE POSTULATION OF A GENERAL SUBSET
OF A SMOOTH SURFACE $X$ WITH $\dim (\mbox{Pic}(X)) >0$

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 smooth projective surface such that $\dim (\mbox{Pic}(X)) >0$. Fix a positive-dimensional family $W$ of line bundles on $X$ and an integer $d>0$. Let $S \subset X$ be a general union of $d$ points. Here we investigate for which $W, d$ the restriction map $H^0(X,L) \to H^0(S,L\vert S)$ has maximal rank for all $L\in W$.

Received: January 15, 2009

AMS Subject Classification: 14K99, 14N05

Key Words and Phrases: zero-dimensional scheme, Picard group

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