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TitleTesting the logarithmic comparison theorem for free divisors.
Author(s) Francisco Jesus Castro-Jimenez, Jose Maria Ucha-Enriquez
TypeArticle in Journal
AbstractWe propose in this work a computational criterion to test if a free divisor D ⊂ Cn verifies the Logarithmic Comparison Theorem (LCT); that is, whether the complex of logarithmic differential forms computes the cohomology of the complement of D in Cn .

For Spencer free divisors D ≡ (f = 0), we solve a conjecture about the generators of the annihilating ideal of 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.
Keywords de Rham cohomology, Logarithmic Comparison Theorem, free divisors, Grobner bases
ISSN1058-6458; 1944-950X/e
URL http://www.tandfonline.com/doi/abs/10.1080/10586458.2004.10504553
JournalExp. Math.
PublisherTaylor & Francis, Philadelphia, PA
Translation No
Refereed No