$D$-Modules Generated by Rational Powers of Holomorphic Functions
| Autor: | Morihiko Saito |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Pure mathematics
Polynomial General Mathematics Open problem Bernstein–Sato polynomial Structure (category theory) Holomorphic function Connection (mathematics) Mathematics - Algebraic Geometry Mathematics::Algebraic Geometry Monodromy FOS: Mathematics Gravitational singularity Algebraic Geometry (math.AG) Mathematics::Symplectic Geometry Mathematics |
| Zdroj: | Publications of the Research Institute for Mathematical Sciences. 57:867-891 |
| ISSN: | 0034-5318 |
| DOI: | 10.4171/prims/57-3-5 |
| Popis: | We prove some sufficient conditions in order that a root of the Bernstein-Sato polynomial contributes to a difference between certain D-modules generated by rational powers of a holomorphic function; for instance, this holds in the case of isolated singularities with semisimple Milnor monodromies. We then construct an example where a root does not contribute to a difference. This also solves an old open problem about the relation between the Milnor monodromy and the exponential of the residue of the Gauss-Manin connection on the saturation of the Brieskorn lattice. This shows that the structure of Brieskorn lattices can be more complicated than one might imagine. Comment: 17 pages, to appear in Publ. RIMS |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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