2000/01/19 by Francisco Javier Gallego, Gallego, Francisco Javier, B. P. Purnaprajna +1 · 1 citation
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.math/0001107
26 pages, AMSTeX
arxiv created 2000/01/19 · arxiv updated 2009/11/30
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.