The biLipschitz geometry of complex curves: an algebraic approach - Archive ouverte HAL
Chapitre D'ouvrage Année : 2020

The biLipschitz geometry of complex curves: an algebraic approach

Résumé

The purpose of these notes is to explain why a generic projection to the plane of a germ of reduced space curve is a biLipschitz homeomorphism for the outer metric. This is related to the fact that all topologically equivalent germs of plane curves are exactly the generic projections of a single space curve. The analytic algebra of this space curve is the algebra of Lipschitz meromorphic functions on any of its generic projections. An application to the geometry of polar curves is given.
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Dates et versions

hal-03874035 , version 1 (27-11-2022)

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Arturo Giles Flores, Otoniel N Silva, Bernard Teissier. The biLipschitz geometry of complex curves: an algebraic approach. Introduction to Lipschitz geometry of singularities, 2280, Springer, pp.217-271, 2020, Lecture Notes in Mathematics,, ⟨10.1007/978-3-030-61807-0_8⟩. ⟨hal-03874035⟩
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