Kodai Mathematical Journal

Mirror symmetry, Kobayashi's duality, and Saito's duality

Wolfgang Ebeling

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Abstract

M. Kobayashi introduced a notion of duality of weight systems. We tone this notion slightly down to a notion called coupling. We show that coupling induces a relation between the reduced zeta functions of the monodromy operators of the corresponding singularities generalizing an observation of K. Saito concerning Arnold's strange duality. We show that the weight systems of the mirror symmetric pairs of M. Reid's list of 95 families of Gorenstein K3 surfaces in weighted projective 3-spaces are strongly coupled. This includes Arnold's strange duality where the corresponding weight systems are strongly dual in Kobayashi's original sense. We show that the same is true for the extension of Arnold's strange duality found by the author and C. T. C. Wall.

Article information

Source
Kodai Math. J., Volume 29, Number 3 (2006), 319-336.

Dates
First available in Project Euclid: 2 November 2006

Permanent link to this document
https://projecteuclid.org/euclid.kmj/1162478765

Digital Object Identifier
doi:10.2996/kmj/1162478765

Mathematical Reviews number (MathSciNet)
MR2278769

Zentralblatt MATH identifier
1133.14035

Citation

Ebeling, Wolfgang. Mirror symmetry, Kobayashi's duality, and Saito's duality. Kodai Math. J. 29 (2006), no. 3, 319--336. doi:10.2996/kmj/1162478765. https://projecteuclid.org/euclid.kmj/1162478765


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