Home > Articles > Published articles > Equigeneric and equisingular families of curves on surfaces |
Date: | 2017 |
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 armatively 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. |
Rights: | Tots els drets reservats. |
Language: | Anglès |
Document: | Article ; recerca ; Versió publicada |
Subject: | Families of singular curves on algebraic surfaces ; Equigeneric and equisingular deformations ; Nodal curves |
Published in: | Publicacions matemàtiques, Vol. 61 Núm. 1 (2017) , p. 175-212 (Articles) , ISSN 2014-4350 |
38 p, 552.6 KB |