Gallego Rodrigo, Francisco JavierPurnaprajna, Bangere P.2023-06-202023-06-2020010075-4102https://hdl.handle.net/20.500.14352/57287The 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 syzygiesengjournal articlehttp://arxiv.org/pdf/math/0001107v1.pdfhttp://arxiv.org/open access512.7Rational surfaceFano varietyline bundleSyzygyproperty NpAdjunction bundlesKoszul cohomologyGeometria algebraica1201.01 Geometría Algebraica