Generation and syzygies of the first secant variety

Peter Vermeire

Generation and syzygies of the first secant variety

Algebraic Geometry 2009-08-04 v3 Commutative Algebra

Authors: Peter Vermeire

Abstract

Under certain effective positivity conditions, we show that the secant variety to a smooth variety satisfies $N_{3,p}$ . For smooth curves, we provide the best possible effective bound on the degree $d$ of the embedding, $d\geq 2g+3+p$ .

Keywords

secant variety syzygies positivity smooth curves effective bound embedding degree

Cite

@article{arxiv.0809.4463,
  title  = {Generation and syzygies of the first secant variety},
  author = {Peter Vermeire},
  journal= {arXiv preprint arXiv:0809.4463},
  year   = {2009}
}

Comments

There was an error in version 2. The degree bound for curves has been re-established, but the proof in higher dimensions has not yet been fixed. See note at the beginning of this version

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