Some examples of non-massive Frobenius manifolds in Singularity Theory

Ignacio de Gregorio

doi:10.1016/j.geomphys.2007.03.003

paper

Some examples of non-massive Frobenius manifolds in Singularity Theory

arXiv:math/0610362 · doi:10.1016/j.geomphys.2007.03.003

Abstract

Let $f,g:\cc^2\ra\cc$ be two quasi-homogeneous polynomials. We compute the $V$ -filtration of the restriction of $f$ to any plane curve $C_{t} = g^{- 1} (t)$ and show that the Gorenstein generator $d x \land d y / d g$ is a primitive form. Using results of A. Douai and C. Sabbah, we conclude that base space of the miniversal unfolding of $f_{t} := f ∣_{C_{t}}$ is a Frobenius manifold. At the singular fibre $C_{0}$ we obtain a non-massive Frobenius manifold.

11 pages