Logarithmic comparison theorem and some Euler homogeneous free divisors
F Castro-Jiménez, J Ucha-Enríquez - Proceedings of the American …, 2005 - ams.org
Proceedings of the American Mathematical Society, 2005•ams.org
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
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
Abstract
Let be a free divisor germ in a complex manifold of dimension . It is an open problem to find out which are the properties required for 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 . We give a family of Euler homogeneous free divisors which, somewhat unexpectedly, does not satisfy the LCT. References
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