Special systems through double points on an algebraic surface

Laface, Antonio

doi:10.1090/S0002-9939-2011-10845-1

Special systems through double points on an algebraic surface
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by Antonio Laface PDF

Proc. Amer. Math. Soc. 139 (2011), 1971-1981 Request permission

Abstract:

Let $S$ be a smooth projective algebraic surface satisfying the following property: $H^i(S,B)=0$ for $i>0$, for any irreducible and reduced curve $B$ of $S$. The aim of this paper is to provide a characterization of special linear systems on $S$ which are singular along a set of double points in very general position. As an application, the dimension of such systems is evaluated in case $S$ is a simple Abelian surface, a $K3$ surface which does not contain elliptic curves or an anticanonical rational surface.

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