Logarithmic Comparison Theorem and some Euler homogeneous free divisors
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- by F. J. Castro-Jiménez and J. M. Ucha-Enríquez PDF
- Proc. Amer. Math. Soc. 133 (2005), 1417-1422 Request permission
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.References
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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
- 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
- © Copyright 2004
American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication. - 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
- MathSciNet review: 2111967