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Linear free divisors and Frobenius manifolds

Part of: Singularities Local theory Representation theory of rings and algebras Theory of singularities and catastrophe theory

Published online by Cambridge University Press:  23 October 2009

Ignacio de Gregorio ,
David Mond  and
Christian Sevenheck
Ignacio de Gregorio
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom (email: degregorio@gmail.com)
David Mond
Affiliation:
Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom (email: D.M.Q.Mond@warwick.ac.uk)
Christian Sevenheck
Affiliation:
Lehrstuhl VI für Mathematik, Universität Mannheim, A6 5, 68131 Mannheim, Germany (email: Christian.Sevenheck@uni-mannheim.de)
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Abstract

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We study linear functions on fibrations whose central fibre is a linear free divisor. We analyse the Gauß–Manin system associated to these functions, and prove the existence of a primitive and homogenous form. As a consequence, we show that the base space of the semi-universal unfolding of such a function carries a Frobenius manifold structure.

Keywords

linear free divisorsprehomogenous vector spacesquiver representationsGauß–Manin systemBrieskorn latticeBirkhoff problemspectral numbersFrobenius manifolds

MSC classification

Secondary: 16G20: Representations of quivers and partially ordered sets 32S40: Monodromy; relations with differential equations and $D$-modules 14B07: Deformations of singularities 58K60: Deformation of singularities
Type
Research Article
Information
Compositio Mathematica , Volume 145 , Issue 5 , September 2009 , pp. 1305 - 1350
Copyright
Copyright © Foundation Compositio Mathematica 2009

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