Mauricio D. Garay

We study germs of $n$-parameter families of functions, that is, function-germs of the type $f : (\mathbb{R}^n \times \mathbb{R}, 0) \to (\mathbb{R}, 0)$ defined on the total space of the trivial bundle $ \mathbb{R}^n \times \mathbb{R} \to \mathbb{R}^n $. There is a natural notion of $V$-equivalence for such function-germs. We introduce the Young diagram of $n$-parameter families satisfying a non-degeneracy condition. We classify all such simple $n$-parameter families and give their versal deformations. This result has direct applications to contact and projective geometry.

2000 Mathematical Subject Classification: 37G25, 14N15.

Keywords: normal form theory, A,D,E classification, bifurcations, wave fronts, parabolic curves, Legendrian mapping.

E-mail:
garay@mathematik.uni-mainz.de