Syzygies, multigraded regularity and toric varieties
Abstract
Using multigraded Castelnuovo-Mumford regularity, we study the equations defining a projective embedding of a variety X. Given globally generated line bundles B1, ..., Bk on X and integers m1, ..., mk, consider the line bundle L := B1m1 ... Bkmk. We give conditions on the mi which guarantee that the ideal of X in P(H0(X,L)) is generated by quadrics and the first p syzygies are linear. This yields new results on the syzygies of toric varieties and the normality of polytopes.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.