Bi-Lipschitz equivalent cones with different degrees

Alexandre Fernandes; Zbigniew Jelonek; José Edson Sampaio

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arXiv · 2309.07078

Bi-Lipschitz equivalent cones with different degrees

Alexandre Fernandes·Zbigniew Jelonek·José Edson Sampaio

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Abstract

We show that for every $k\ge 3$ there exist complex algebraic cones of dimension $k$ with isolated singularities, which are bi-Lipschitz and semi-algebraically equivalent but they have different degrees. We also prove that homeomorphic projective hypersurfaces with dimension greater than 2 have the same degree. In the final part of the paper, we classify links of real cones with base $\mathbb{P}^1\times \mathbb{P}^2.$ As an application we give an example of three four dimensional real algebraic cones in $\mathbb{R}^8$ with isolated singularity which are semi-algebraically and bi-Lipschitz equivalent but they have non-homeomorphic bases.

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BibTeX RIS

Alexandre Fernandes, Zbigniew Jelonek, José Edson Sampaio. 2023-09-13. Bi-Lipschitz equivalent cones with different degrees. https://arxiv.org/abs/2309.07078

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