On Syzygies of Projected Algebraic Curves

Wanseok Lee, Euisung Park

Research output: Contribution to journalArticlepeer-review


Let C ⊂ ℙr be a linearly normal projective integral curve of arithmetic genus g ≥ 1 and degree d = 2g + 1 + p for some p ≥ 1. It is well known that C is cut out by quadric and satisfies Green-Lazarsfeld's property Np. Recently it is known that for any q ∈ ℙr\C such that the linear projection πq: C → ℙr-1 of C from q is an embedding, the projected image Cq:= πq(C) ⊂ ℙr-1 is 3-regular, and hence its homogeneous ideal is generated by quadratic and cubic equations. In this article we study the problem when Cq is still cut out by quadrics. Our main result in this article shows that if the relative location of q with respect to C is general then the homogeneous ideal of C q is still generated by quadrics and the syzygies among them are generated by linear syzygies for the first a few steps.

Original languageEnglish
Pages (from-to)2092-2099
Number of pages8
JournalCommunications in Algebra
Issue number6
Publication statusPublished - 2013 May


  • Linear projection
  • Minimal free resolution
  • Projective curve

ASJC Scopus subject areas

  • Algebra and Number Theory


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