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Some results on rational surfaces and Fano varieties

Francisco Javier Gallego·B. P. Purnaprajna
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Abstract

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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BibTeXRIS

Francisco Javier Gallego, B. P. Purnaprajna. 2000-01-19. Some results on rational surfaces and Fano varieties. https://arxiv.org/abs/math/0001107

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