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Linear free divisors and Frobenius manifolds

Published online by Cambridge University Press:  23 October 2009

Ignacio de Gregorio
Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom (email:
David Mond
Mathematics Institute, University of Warwick, Coventry CV4 7AL, United Kingdom (email:
Christian Sevenheck
Lehrstuhl VI für Mathematik, Universität Mannheim, A6 5, 68131 Mannheim, Germany (email:
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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.

Research Article
Copyright © Foundation Compositio Mathematica 2009


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