Syzygies and logarithmic vector fields along plane curves

Alexandru Dimca[1]; Edoardo Sernesi[2]

  • [1] Université Nice Sophia Antipolis, CNRS, LJAD, UMR 7351 Parc Valrose, 06108 Nice, Cedex 02, France
  • [2] Dipartimento di Matematica e Fisica, Università Roma Tre, Largo S. L. Murialdo 1, 00146 Roma, Italy

Journal de l’École polytechnique — Mathématiques (2014)

  • Volume: 1, page 247-267
  • ISSN: 2270-518X

Abstract

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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.

How to cite

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Dimca, Alexandru, and Sernesi, Edoardo. "Syzygies and logarithmic vector fields along plane curves." Journal de l’École polytechnique — Mathématiques 1 (2014): 247-267. <http://eudml.org/doc/275573>.

@article{Dimca2014,
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.},
affiliation = {Université Nice Sophia Antipolis, CNRS, LJAD, UMR 7351 Parc Valrose, 06108 Nice, Cedex 02, France; Dipartimento di Matematica e Fisica, Università Roma Tre, Largo S. L. Murialdo 1, 00146 Roma, Italy},
author = {Dimca, Alexandru, Sernesi, Edoardo},
journal = {Journal de l’École polytechnique — Mathématiques},
keywords = {Syzygy; plane curve; logarithmic vector fields; stable bundle; free divisor; Torelli property},
language = {eng},
pages = {247-267},
publisher = {École polytechnique},
title = {Syzygies and logarithmic vector fields along plane curves},
url = {http://eudml.org/doc/275573},
volume = {1},
year = {2014},
}

TY - JOUR
AU - Dimca, Alexandru
AU - Sernesi, Edoardo
TI - Syzygies and logarithmic vector fields along plane curves
JO - Journal de l’École polytechnique — Mathématiques
PY - 2014
PB - École polytechnique
VL - 1
SP - 247
EP - 267
AB - 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.
LA - eng
KW - Syzygy; plane curve; logarithmic vector fields; stable bundle; free divisor; Torelli property
UR - http://eudml.org/doc/275573
ER -

References

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