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Special systems through double points on an algebraic surface


Author: Antonio Laface
Journal: Proc. Amer. Math. Soc. 139 (2011), 1971-1981
MSC (2010): Primary 14C20
DOI: https://doi.org/10.1090/S0002-9939-2011-10845-1
Published electronically: January 21, 2011
MathSciNet review: 2775373
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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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Additional Information

Antonio Laface
Affiliation: Departamento de Matemática, Universidad de Concepción, Casilla 160-C, Concepción, Chile
Email: alaface@udec.cl

DOI: https://doi.org/10.1090/S0002-9939-2011-10845-1
Keywords: Linear systems, double points, secant varieties
Received by editor(s): March 15, 2007
Received by editor(s) in revised form: December 27, 2007, August 21, 2009, and June 3, 2010
Published electronically: January 21, 2011
Communicated by: Ted Chinburg
Article copyright: © Copyright 2011 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.