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Logarithmic Comparison Theorem and some Euler homogeneous free divisors


Authors: F. J. Castro-Jiménez and J. M. Ucha-Enríquez
Journal: Proc. Amer. Math. Soc. 133 (2005), 1417-1422
MSC (2000): Primary 32S20; Secondary 14F10, 32S40
DOI: https://doi.org/10.1090/S0002-9939-04-07678-6
Published electronically: November 1, 2004
MathSciNet review: 2111967
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Abstract | References | Similar Articles | Additional Information

Abstract: Let $D,x$ be a free divisor germ in a complex manifold $X$ of dimension $n>2$. It is an open problem to find out which are the properties required for $D,x$ to satisfy the so-called Logarithmic Comparison Theorem (LCT), that is, when the complex of logarithmic differential forms computes the cohomology of the complement of $D,x$. We give a family of Euler homogeneous free divisors which, somewhat unexpectedly, does not satisfy the LCT.


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Additional Information

F. J. Castro-Jiménez
Affiliation: Departamento de Álgebra, Facultad de Matemáticas, Universidad de Sevilla, Apdo 1160, E-41080 Sevilla, Spain
Email: castro@us.es

J. M. Ucha-Enríquez
Affiliation: Departamento de Álgebra, Facultad de Matemáticas, Universidad de Sevilla, Apdo 1160, E-41080 Sevilla, Spain
Email: ucha@us.es

DOI: https://doi.org/10.1090/S0002-9939-04-07678-6
Keywords: Free divisor, Logarithmic Comparison Theorem, $D$-modules, Euler-homogeneous divisor
Received by editor(s): July 21, 2003
Received by editor(s) in revised form: January 8, 2004
Published electronically: November 1, 2004
Additional Notes: This work was partially supported by DGESIC BFM-2001-3164 and FQM-333.
Communicated by: Michael Stillman
Article copyright: © Copyright 2004 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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