We propose in this work a computational criterion to test if a free divisor {\small $D\subset {\bf C}^n$} verifies the Logarithmic Comparison Theorem (LCT); that is, whether the complex of logarithmic differential forms computes the cohomology of the complement of {\small $D$} in {\small ${\bf C}^n$}.
¶ For Spencer free divisors {\small $D\equiv(f=0)$}, we solve a conjecture about the generators of the annihilating ideal of {\small $1/f$} and make a conjecture on the nature of Euler homogeneous free divisors which verify LCT. In addition, we provide examples of free divisors defined by weighted homogeneous polynomials that are not locally quasi-homogeneous.
Publié le : 2004-05-14
Classification:
de Rham cohomology,
Logarithmic Comparison Theorem,
free divisors,
Gröbner bases,
14F50,
32C38,
32C35,
13Pxx,
68W30
@article{1109106436,
author = {Castro-Jim\'enez, F. J. and Ucha-Enr\'\i quez, J. M.},
title = {Testing the Logarithmic Comparison Theorem for Free Divisors},
journal = {Experiment. Math.},
volume = {13},
number = {1},
year = {2004},
pages = { 441-449},
language = {en},
url = {http://dml.mathdoc.fr/item/1109106436}
}
Castro-Jiménez, F. J.; Ucha-Enríquez, J. M. Testing the Logarithmic Comparison Theorem for Free Divisors. Experiment. Math., Tome 13 (2004) no. 1, pp. 441-449. http://gdmltest.u-ga.fr/item/1109106436/