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Linear free divisors and Frobenius manifolds. (English) Zbl 1238.32022
Summary: 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 homogeneous form. As a consequence, we show that the base space of the semi-universal unfolding of such a function carries a Frobenius manifold structure.

MSC:
32S40 Monodromy; relations with differential equations and \(D\)-modules (complex-analytic aspects)
14B07 Deformations of singularities
58K60 Deformation of singularities
Software:
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