Equigeneric and equisingular families of curves on surfaces
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...
| Autores: | , |
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| Tipo de recurso: | artículo |
| Fecha de publicación: | 2017 |
| País: | España |
| Institución: | Universitat Autònoma de Barcelona |
| Repositorio: | Dipòsit Digital de Documents de la UAB |
| Idioma: | inglés |
| OAI Identifier: | oai:ddd.uab.cat:168349 |
| Acceso en línea: | https://ddd.uab.cat/record/168349 https://dx.doi.org/urn:doi:10.5565/PUBLMAT_61117_07 |
| Access Level: | acceso abierto |
| Palabra clave: | Families of singular curves on algebraic surfaces Equigeneric and equisingular deformations Nodal curves |
| Sumario: | 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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