Syzygies and logarithmic vector fields along plane curves

Alexandru Dimca; Edoardo Sernesi

Syzygies and logarithmic vector fields along plane curves

Algebraic Geometry 2017-08-30 v2 Commutative Algebra

Authors: Alexandru Dimca , Edoardo Sernesi

Abstract

We investigate the relations between the syzygies of the Jacobian ideal of the defining equation for a plane curve $C$ and the stability of the sheaf of logarithmic vector fields along $C$ , the freeness of the divisor $C$ and the Torelli properties of $C$ (in the sense of Dolgachev-Kapranov). We show in particular that curves with a small number of nodes and cusps are Torelli in this sense.

Keywords

algebraic curves hyperelliptic curves curves

Cite

@article{arxiv.1401.6838,
  title  = {Syzygies and logarithmic vector fields along plane curves},
  author = {Alexandru Dimca and Edoardo Sernesi},
  journal= {arXiv preprint arXiv:1401.6838},
  year   = {2017}
}

Comments

version 2: some typos corrected and references updated

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