Equigeneric and equisingular families of curves on surfaces
Dedieu, Thomas (Université Paul Sabatier (França). Institut de Mathématiques de Toulouse)
Sernesi, E. (Universitá Roma Tre. Dipartimento di Matematica e Fisica)

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.
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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

Adreça alternativa: https://raco.cat/index.php/PublicacionsMatematiques/article/view/316083
DOI: 10.5565/PUBLMAT_61117_07

38 p, 552.6 KB

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