Publicacions Matemàtiques

Equigeneric and equisingular families of curves on surfaces

T. Dedieu and E. Sernesi

Full-text: Access denied (no subscription detected)

We're sorry, but we are unable to provide you with the full text of this article because we are not able to identify you as a subscriber. If you have a personal subscription to this journal, then please login. If you are already logged in, then you may need to update your profile to register your subscription. Read more about accessing full-text

Abstract

We investigate the following question: let $C$ be an integral curve contained in a smooth complex algebraic surface $X$; is it possible to deform $C$ in $X$ into a nodal curve while preserving its geometric genus?

We affirmatively answer it in most cases when $X$ is a Del Pezzo or Hirzebruch surface (this is due to Arbarello and Cornalba, Zariski, and Harris), and in some cases when $X$ is a $K3$ surface. Partial results are given for all surfaces with numerically trivial canonical class. We also give various examples for which the answer is negative.

Article information

Source
Publ. Mat., Volume 61, Number 1 (2017), 175-212.

Dates
Received: 20 May 2015
Revised: 30 July 2015
First available in Project Euclid: 22 December 2016

Permanent link to this document
https://projecteuclid.org/euclid.pm/1482375629

Digital Object Identifier
doi:10.5565/PUBLMAT_61117_07

Mathematical Reviews number (MathSciNet)
MR3590119

Zentralblatt MATH identifier
1374.14025

Subjects
Primary: 14H10: Families, moduli (algebraic)
Secondary: 14H20: Singularities, local rings [See also 13Hxx, 14B05] 14B07: Deformations of singularities [See also 14D15, 32S30]

Keywords
Families of singular curves on algebraic surfaces equigeneric and equisingular deformations nodal curves

Citation

Dedieu, T.; Sernesi, E. Equigeneric and equisingular families of curves on surfaces. Publ. Mat. 61 (2017), no. 1, 175--212. doi:10.5565/PUBLMAT_61117_07. https://projecteuclid.org/euclid.pm/1482375629


Export citation