Logarithmic cohomology of the complement of a plane curve
Let D, x be a plane curve germ. We prove that the complex Ω•(log D)x computes the cohomology of the complement of D, x only if D is quasihomogeneous. This is a partial converse to a theorem of F.J. Castro-Jiménez, D. Mond and L. Narváez-Macarro. Cohomology of the complement of a free divisor. Transa...
| Autores: | , , , |
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| Tipo de recurso: | artículo |
| Estado: | Versión enviada para evaluación y publicación |
| Fecha de publicación: | 2002 |
| País: | España |
| Institución: | Universidad de Sevilla (US) |
| Repositorio: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/48439 |
| Acceso en línea: | http://hdl.handle.net/11441/48439 https://doi.org/10.1007/s00014-002-8330-6 |
| Access Level: | acceso abierto |
| Palabra clave: | Free divisor Logarithmic de Rham complex Plane curve Local quasi-homogeneity |
| Sumario: | Let D, x be a plane curve germ. We prove that the complex Ω•(log D)x computes the cohomology of the complement of D, x only if D is quasihomogeneous. This is a partial converse to a theorem of F.J. Castro-Jiménez, D. Mond and L. Narváez-Macarro. Cohomology of the complement of a free divisor. Transactions of the A.M.S., 348 (1996), 3037– 3049, which asserts that this complex does compute the cohomology of the complement, whenever D is a locally weighted homogeneous free divisor (and so in particular when D is a quasihomogeneous plane curve germ). We also give an example of a free divisor in D ⊂ C3 which is not locally weighted homogeneous, but for which this (second) assertion continues to hold. |
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