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This article is cited in 2 scientific papers (total in 2 papers)
Monodromy of dual invertible polynomials
W. Ebelinga, S. M. Gusein-Zadeb a Leibniz Universität Hannover, Institut für Algebraische Geometrie, Hannover, Germany
b Moscow State University, Faculty of Mechanics and Mathematics, Moscow, Russia
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 $f^T$.
Key words and phrases:
invertible polynomials, monodromy, zeta functions, Saito duality.
Received: September 9, 2010
Citation:
W. Ebeling, S. M. Gusein-Zade, “Monodromy of dual invertible polynomials”, Mosc. Math. J., 11:3 (2011), 463–472
Linking options:
https://www.mathnet.ru/eng/mmj427 https://www.mathnet.ru/eng/mmj/v11/i3/p463
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Abstract page: | 238 | References: | 67 |
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