Using miiltigraded Castelnuovo-Mumford regularity, we study the equations denning a projective embedding of a variety X. Given globally generated line bundles B1,..., Bl on X and m1,..., m l ∈ N, consider the line bundle L :- B1m1 ⊗...⊗Blml. We give conditions on the m i which guarantee that the ideal of X in ℙ(H0(X, L)*) is generated by quadrics and that the first p syzygies are linear. This yields new results on the syzygies of toric varieties and the normality of polytopes.
- Caatelnuovo-Mumford regularity
- Toric variety
ASJC Scopus subject areas
- Algebra and Number Theory