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A duality approach to the symmetry of Bernstein-Sato polynomials of free divisors

 

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Opened Access A duality approach to the symmetry of Bernstein-Sato polynomials of free divisors
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Author: Narváez Macarro, Luis
Department: Universidad de Sevilla. Departamento de álgebra
Date: 2015-08-20
Published in: Advances in Mathematics, 281, 1242-1273.
Document type: Article
Abstract: In this paper we prove that the Bernstein-Sato polynomial of any free divisor for which the D[s]-module D[s]h s admits a Spencer logarithmic resolution satisfies the symmetry property b(−s−2) = ±b(s). This applies in particular to locally quasi-homogeneous free divisors (for instance, to free hyperplane arrangements), or more generally, to free divisors of linear Jacobian type. We also prove that the Bernstein-Sato polynomial of an integrable logarithmic connection E and of its dual E ∗ with respect to a free divisor of linear Jacobian type are related by the equality bE(s) = ±bE∗ (−s − 2). Our results are based on the behaviour of the modules D[s]h s and D[s]E[s]h s under duality.
Cite: Narváez Macarro, L. (2015). A duality approach to the symmetry of Bernstein-Sato polynomials of free divisors. Advances in Mathematics, 281, 1242-1273.
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URI: http://hdl.handle.net/11441/42931

DOI: http://dx.doi.org/10.1016/j.aim.2015.06.012

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