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Strange duality of weighted homogeneous polynomials

Part of: Surfaces and higher-dimensional varieties Singularities Algebraic groups

Published online by Cambridge University Press:  26 April 2011

Wolfgang Ebeling  and
Atsushi Takahashi
Wolfgang Ebeling
Affiliation:
Institut für Algebraische Geometrie, Leibniz Universität Hannover, Postfach 6009, D-30060 Hannover, Germany (email: ebeling@math.uni-hannover.de)
Atsushi Takahashi
Affiliation:
Department of Mathematics, Graduate School of Science, Osaka University, Toyonaka, Osaka 560-0043, Japan (email: takahashi@math.sci.osaka-u.ac.jp)
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Abstract

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We consider a mirror symmetry between invertible weighted homogeneous polynomials in three variables. We define Dolgachev and Gabrielov numbers for them and show that we get a duality between these polynomials generalizing Arnold’s strange duality between the 14 exceptional unimodal singularities.

Keywords

mirror symmetrysingularityinvertible polynomialweighted projective linestrange dualityDolgachev numbersGabrielov numbers

MSC classification

Secondary: 14J33: Mirror symmetry 32S25: Surface and hypersurface singularities 14L30: Group actions on varieties or schemes (quotients)
Type
Research Article
Information
Compositio Mathematica , Volume 147 , Issue 5 , September 2011 , pp. 1413 - 1433
Copyright
Copyright © Foundation Compositio Mathematica 2011

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