Asymptotic Np property of rational surfaces

Details Asymptotic Np property of rational surfaces Asymptotic Np property of rational surfaces

2001-02-28

arxiv.org/abs/math/0102224v2

Mathematics

Algebraic Geometry

7 pages

Scientific paper

In this paper, we examine Green and Lazarsfeld's Np property for rational surfaces obtained by blowing up the projective plane P^2 at a subscheme of fat points Z. We show that these surfaces, embedded into projective spaces by linear system of plane curves of degree t containing Z, possess property Np for all t >> 0. This gives a positive answer to a conjecture of Geramita and Gimigliano. Our bound for the values t is better than the conjectural value, which is \sigma(Z) + p.

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