Some results on rational surfaces and Fano varieties

Details Some results on rational surfaces and Fano varieties Some results on rational surfaces and Fano varieties

2000-01-19

arxiv.org/abs/math/0001107v1

Mathematics

Algebraic Geometry

26 pages, AMSTeX

Scientific paper

The goal of this article is to study the equations and syzygies of embeddings of rational surfaces and certain Fano varieties. Given a rational surface X and an ample and base-point-free line bundle L on X, we give an optimal numerical criterion for L to satisfy property Np. This criterion turns out to be a characterization of property Np if X is anticanonical. We also prove syzygy results for adjunction bundles and a Reider type theorem for higher syzygies. For certain Fano varieties we also prove results on very ampleness and higher syzygies.

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