On syzygies of Veronese embedding of arbitrary projective varieties

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4 Citations (Scopus)


For a very ample line bundle L on a projective scheme X, let φLℓ : X {right arrow, hooked} P H0 (X, L), ℓ ≥ 1, be the embedding defined by the complete linear series | L |. In this paper we study the problem how the Castelnuovo-Mumford regularity of φL (X) effects on the defining equations of φLℓ (X) and the syzygies among them. We show that if φL (X) ⊂ P H0 (X, L) is m-regular, then (X, L) satisfies property N2 ℓ - m + 1 for frac(m, 2) ≤ ℓ ≤ m - 2, and (X, L) satisfies property N for all ℓ ≥ m - 1.

Original languageEnglish
Pages (from-to)108-121
Number of pages14
JournalJournal of Algebra
Issue number1
Publication statusPublished - 2009 Jul 1


  • Algebraic geometry
  • Minimal free resolution
  • Projective variety

ASJC Scopus subject areas

  • Algebra and Number Theory


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