On simple families of functions and their Legendrian mappings

• Autores: Mauricio D. Garay
• Localización: Proceedings of the London Mathematical Society, ISSN 0024-6115, Vol. 88, Nº 1, 2004, págs. 148-184
• Idioma: inglés
• DOI: 10.1112/s0024611503014370
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• Resumen

  • 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.