Syzygies, multigraded regularity and toric varieties

Milena Hering*, Hal Schenck, Gregory G. Smith

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract / Description of output

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.

Original languageEnglish
Pages (from-to)1499-1506
Number of pages8
JournalCompositio Mathematica
Issue number6
Publication statusPublished - 24 Nov 2006

Keywords / Materials (for Non-textual outputs)

  • Caatelnuovo-Mumford regularity
  • Syzygy
  • Toric variety


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