IJPAM: Volume 34, No. 1 (2007)


Marco Franciosi
Department of Applied Mathematics
University of Pisa
1C, Via Buonarroti, Pisa, I-56127, ITALY
e-mail: franciosi@dma.unipi.it
url: https://www.ing.unipi.it/ d8702/

Abstract.Let $C$ be a numerically connected curve lying on a smooth algebraic surface. We show that an invertible sheaf $\sH\numeq \om_{C}\otimes \sA$ is normally generated on $C$ if $\sA$ is an ample invertible sheaf of degree $\geq 3$.

As a corollary we show that on a smooth algebraic surface of general type the invertible sheaf $K_S^{\otimes 3}$ yields a projectively normal embedding of $S$ assuming $K_S$ ample, $(K_S)^2\ge3$, $p_g(S) \geq 2$ and $q(S)=0$.

Received: October 20, 2006

AMS Subject Classification: 14H45, 14C20, 14J29

Key Words and Phrases: arithmetically Cohen-Macaulay projective scheme, algebraic curve, algebraic surface

Source: International Journal of Pure and Applied Mathematics
ISSN: 1311-8080
Year: 2007
Volume: 34
Issue: 1