IJPAM: Volume 46, No. 4 (2008)

${\bf {P}}^{n-1}\times C$ WITH $C$ A SMOOTH CURVE

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

Abstract.Fix a smooth genus $q>0$ curve, an integral $(n-1)$-dimensional variety $Y$ and an ample $H\in \mbox{\rm Pic}(Y)$ such that $h^i(Y,H^{\otimes t})=0$ for all $1 \le i \le n-2$ and all $t\in \mathbb {Z}$. Let $E$ be a vector bundle on $X:= Y\times C$. We will say that $E$ is ACM if $h^i(X,E\otimes L)=0$ for all $1 \le i \le n-1$ and certain $L\in \mbox{\rm Pic}(X)$ constructed from $H$ and $ \mbox{\rm Pic}(C)$. Here we study ACM vector bundles on $X$, mainly when $Y = {\bf {P}}^{n-1}$ and $\mbox{\rm rank}(E) \le n-2$.

Received: April 5, 2008

AMS Subject Classification: 14J60

Key Words and Phrases: vector bundle, ACM bundle, arithmetically Cohen-Macaulay vector bundle

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2008
Volume: 46
Issue: 4