Logarithmic Comparison Theorem and some Euler homogeneous free divisors
F.J. Castro-Jiménez,José Maria Ucha-Enriquez +1 more
- Vol. 133, Iss: 5, pp 1417-1422
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In this article, the authors give a family of Euler homogeneous free divisors which, somewhat unexpectedly, does not satisfy the Logarithmic Comparison Theorem (LCT).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.read more
Citations
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Linear free divisors and the global logarithmic comparison theorem
TL;DR: In this paper, the GLCT holds for LFDs arising naturally as discriminants in quiver representation spaces (of real Schur roots) and is shown to hold for all linear free divisors for n at most 4.
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On meromorphic functions defined by a differential system of order 1, II
TL;DR: In this paper, a nonzero germ h of holomorphic function on (C^n, 0) hypersurfaces with an isolated singularity is verified if and only if h is weighted homogeneous and -1 is the only integral root of its Bernstein-Sato polynomial.
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On meromorphic functions defined by a differential system of order $1$
TL;DR: In this paper, a nonzero germ h of holomorphic function on (C n, 0) hypersurfaces with isolated singularity is verified if and only if h is weighted homogeneous and −1 is the only integral root of its Bernstein-Sato polynomial.
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On the formal structure of logarithmic vector fields
Michel Granger,Mathias Schulze +1 more
TL;DR: In this article, it was shown that a free divisor in a three dimensional complex manifold must be Euler homogeneous in a strong sense if the cohomology of its complement is the hypercohomology of the logarithmic differential forms.
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Embedded q-resolutions and yomdin-lê surface singularities
TL;DR: In this article, the generalized A'Campo's formula is applied to compute the characteristic polynomial of the embedded Q-resolution of a Yomdin-Le surface singularity (V, 0) in terms of a (global) embedded Qresolution of its tangent cone by means of just weighted blow-ups at points.
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