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2004 Testing the Logarithmic Comparison Theorem for Free Divisors
F. J. Castro-Jiménez, J. M. Ucha-Enríquez
Experiment. Math. 13(4): 441-449 (2004).

Abstract

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.

Citation

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F. J. Castro-Jiménez. J. M. Ucha-Enríquez. "Testing the Logarithmic Comparison Theorem for Free Divisors." Experiment. Math. 13 (4) 441 - 449, 2004.

Information

Published: 2004
First available in Project Euclid: 22 February 2005

zbMATH: 1071.14024
MathSciNet: MR2118269

Subjects:
Primary: 14F50
Secondary: 13Pxx , 32C35 , 32C38 , 68W30

Keywords: de Rham cohomology , free divisors , Gröbner bases , Logarithmic Comparison Theorem

Rights: Copyright © 2004 A K Peters, Ltd.

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