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Página principal > Artículos > Artículos publicados > Equigeneric and equisingular families of curves on surfaces |
Fecha: | 2017 |
Resumen: | 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. |
Derechos: | Tots els drets reservats. |
Lengua: | Anglès |
Documento: | Article ; recerca ; Versió publicada |
Materia: | Families of singular curves on algebraic surfaces ; Equigeneric and equisingular deformations ; Nodal curves |
Publicado en: | Publicacions matemàtiques, Vol. 61 Núm. 1 (2017) , p. 175-212 (Articles) , ISSN 2014-4350 |
38 p, 552.6 KB |