Linear free divisors and Frobenius manifolds

Abstract

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.

37 pages

References in corpus (3)

• Stokes Matrices and Monodromy of the Quantum Cohomology of Projective Spaces
• A construction of Frobenius manifolds with logarithmic poles and applications
• Some examples of non-massive Frobenius manifolds in Singularity Theory

Cited by in corpus (6)

• Normal crossing properties of complex hypersurfaces via logarithmic residues
• Irregular Hodge filtration of some confluent hypergeometric systems
• Examples of hypergeometric twistor $\mathcal{D}$-modules
• Local cohomology of logarithmic forms
• Hodge ideals of free divisors
• Tautological systems and free divisors