Deforming the weighted-homogeneous foliation, and trivializing families of semi-weighted homogeneous ICIS

2024/09/15 by Dmitry Kerner, Rodrigo E. Mendes, Kerner, Dmitry +1 · 1 citation
Computer Science · #Constraint Satisfaction and Optimization

paper · pdf · doi:10.48550/arxiv.2409.09764

Abstract

Let X_o be a weighted-homogeneous complete intersection germ in (R^N,o) or (C^N,o), with arbitrary singularities, possibly non-reduced. Take the foliation of the ambient space by weighted-homogeneous real arcs, \ga_s. Take a deformation of X_o by higher order terms, X_t. Does the foliation \ga_s deform compatibly with X_t? We identify the ``obstruction locus", Σin X_o, outside of which such a deformation does exist, and possesses exceptionally nice properties. Using this deformed foliation we construct a contact trivialization of the family of defining equations by a homeomorphism that is real analytic (resp. Nash) off the origin, differentiable at the origin, whose presentation in weighted-polar coordinates is globally real-analytic (resp. globally Nash), and with controlled Lipschitz/C¹-properties.

Cited by

• Andreotti-Frankel-Hamm theorem for morphisms of algebraic varieties

Related

• Fast vanishing cycles on perturbations of complex weighted-homogeneous complete intersection germs
• Invariant Hypersurfaces and Nodal Components of Foliations
• Germes de feuilletages présentables du plan complexe
• The Galoisian envelope of a germ of foliation: the quasi-homogeneous case
• Taut foliations