Monodromy of dual invertible polynomials

Details Monodromy of dual invertible polynomials Monodromy of dual invertible polynomials

2010-08-24

arxiv.org/abs/1008.4021v3

Mathematics

Algebraic Geometry

Scientific paper

A generalization of Arnold's strange duality to invertible polynomials in three variables by the first author and A.Takahashi includes the following relation. For some invertible polynomials $f$ the Saito dual of the reduced monodromy zeta function of $f$ coincides with a formal "root" of the reduced monodromy zeta function of its Berglund-H\"ubsch transpose $f^T$. Here we give a geometric interpretation of "roots" of the monodromy zeta function and generalize the above relation to all non-degenerate invertible polynomials in three variables and to some polynomials in an arbitrary number of variables in a form including "roots" of the monodromy zeta functions both of $f$ and $f^T$.

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