Monodromy of dual invertible polynomials

2010/08/24 by Ebeling, Wolfgang, Gusein-Zade, Sabir M.
#14J33 #32S05 #32S40 #Algebraic Geometry (math.AG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1008.4021

Abstract

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-Hübsch 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.

Related

• Introduction to the monodromy conjecture
• Orbifold zeta functions for dual invertible polynomials
• The monodromy conjecture for zeta functions associated to ideals in dimension two
• Strange duality and polar duality
• Monodromy eigenvalues and zeta functions with differential forms