A duality approach to the symmetry of Bernstein-Sato polynomials of free divisors
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 hyperp...
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| Format: | article |
| Status: | Versión enviada para evaluación y publicación |
| Publication Date: | 2015 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/42931 |
| Online Access: | http://hdl.handle.net/11441/42931 https://doi.org/10.1016/j.aim.2015.06.012 |
| Access Level: | Open access |
| Keyword: | Bernstein-Sato polynomials Free divisors Logarithmic differential operators Spencer resolutions Lie-Rinehart algebras Logarithmic connections |
| Summary: | 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. |
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