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arXiv · 2104.06894

On algebraic bi-Lipschitz homeomorphisms

Zbigniew Jelonek
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Abstract

Let $X\subset \mathbb{C}^n; Y\subset \mathbb{C}^m$ be closed affine varieties and let $ϕ: X\to Y$ be an algebraic bi-Lipschitz homeomorphism. Then ${\rm deg}\ X={\rm deg}\ Y.$ Similarly, let $(X,0)\subset (\mathbb{C}^n,0), (Y,0)\subset (\mathbb{C}^m,0)$ be germs of analytic sets and let $f: (X,0)\to (Y,0)$ be a c-holomorphic and bi-Lipschitz mapping. Then ${\rm mult}_0 \ X= {\rm mult }_0 \ Y.$ Finally we show that the normality is not a bi-Lipschitz invariant.

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Zbigniew Jelonek. 2021-05-06. On algebraic bi-Lipschitz homeomorphisms. https://arxiv.org/abs/2104.06894

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