Syzygies, multigraded regularity and toric varieties

Milena Hering, Hal Schenck, Gregory G. Smith

Research output: Contribution to journalArticle


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 (US)
Pages (from-to)1499-1506
Number of pages8
JournalCompositio Mathematica
Issue number6
StatePublished - Nov 1 2006


  • Caatelnuovo-Mumford regularity
  • Syzygy
  • Toric variety

ASJC Scopus subject areas

  • Algebra and Number Theory

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