A. Fernandes

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math.AG2024

On metric equivalence of the Brieskorn-Pham hypersurfaces

Alexandre Fernandes, Zbigniew Jelonek, José Edson Sampaio

We show that two bi-Lipschitz equivalent Brieskorn-Pham hypersurfaces have the same multiplicities at $0$ . Moreover we show that if two algebraic $(n - 1)$ -dimensional cones $P, R\su…

math.AG2024

Hölder invariance of the Henry-Parusinski invariant

Alexandre Fernandes, José Edson Sampaio, Joserlan Perote da Silva

In this article, we show the Hölder invariance of the Henry-Parusinski invariant. For a single germ $f$ , the Henry-Parusinski invariant of $f$ is given in terms of the leading c…

math.AG2023

Bi-Lipschitz equivalent cones with different degrees

Alexandre Fernandes, Zbigniew Jelonek, José Edson Sampaio

We show that for every $k \geq 3$ there exist complex algebraic cones of dimension $k$ with isolated singularities, which are bi-Lipschitz and semi-algebraically equivalent but they…