RT Journal Article T1 Some results on rational surfaces and Fano varieties. A1 Gallego Rodrigo, Francisco Javier A1 Purnaprajna, Bangere P. AB 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 N-p. This criterion turns out to be a characterization of property N-p if X is anticanonical. We also prove syzygy results for adjunction bundles and a Reider type theorem for higher syzygies PB Walter de Gruyter & co SN 0075-4102 YR 2001 FD 2001 LK https://hdl.handle.net/20.500.14352/57287 UL https://hdl.handle.net/20.500.14352/57287 LA eng DS Docta Complutense RD 8 abr 2025