Abstract
The Bernstein polynomial of an isolated hypersurface singularity has subtle relations with the spectral numbers and the Tjurina number. To study these relations we use the Gauβ–Manin connection, Malgrange's description of the Bernstein polynomial and ideas of M. Saito. A general discussion of μ-constant families leads to manageable methods for explicit calculations, which we use on a number of examples. We introduce a matrix which determines simultaneously the Bernstein polynomial and the Tjurina number.
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Hertling, C., Stahlke, C. Bernstein Polynomial and Tjurina Number. Geometriae Dedicata 75, 137–176 (1999). https://doi.org/10.1023/A:1005012325661
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DOI: https://doi.org/10.1023/A:1005012325661