2015/07/07 by Morihiko Saito, Saito, Morihiko
Mathematics · #Algebraic Geometry (math.AG) #FOS: Mathematics #math.AG
paper · pdf · doi:10.48550/arxiv.1507.01877
17 pages, to appear in Publ. RIMS
arxiv created 2019/03/10 · arxiv updated 2019/03/12
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.