Article
Logarithmic cohomology of the complement of a plane curve
Author/s | Calderón Moreno, Francisco Javier
![]() ![]() ![]() ![]() ![]() ![]() ![]() Mond, David Narváez Macarro, Luis ![]() ![]() ![]() ![]() ![]() ![]() ![]() Castro Jiménez, Francisco Jesús ![]() ![]() ![]() ![]() ![]() ![]() ![]() |
Department | Universidad de Sevilla. Departamento de álgebra |
Publication Date | 2002-03 |
Deposit Date | 2016-11-10 |
Published in |
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Abstract | 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 ... 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. |
Funding agencies | Ministerio de Educación y Ciencia (MEC). España Engineering and Physical Sciences Research Council (UK) |
Project ID. | PB97-0723
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Citation | Calderón Moreno, F.J., Mond, D., Narváez Macarro, L. y Castro Jiménez, F.J. (2002). Logarithmic cohomology of the complement of a plane curve. Commentarii Mathematici Helvetici, 77 (1), 24-38. |
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