Adjoint linear systems on a surface of general type in positive characteristic

Tohru Nakashima

Vol. 160 (1993), No. 1, 129–132

DOI: 10.2140/pjm.1993.160.129

Abstract

Let X be a minimal surface of general type defined over an algebraically closed field of positive characteristic p . For a given divisor D, we consider the spannedness properties of adjoint linear systems |K + D| on X. Under some numerical conditions on p and D, the failure of spannedness of |K + D| implies the existence of divisors with special properties. This leads to the following result: Let L be an ample line bundle and assume p ≥ 5. Then |m(K + L)| is base point free for m ≥ 2 and very ample for m ≥ 3. Our proof is based on a technique of Shepherd-Barron using unstable vector bundles.

Mathematical Subject Classification 2000

Primary: 14J60

Secondary: 14C20, 14J29

Milestones

Received: 18 March 1991

Published: 1 September 1993