2023/09/13 by Alexandre Fernandes, Zbigniew Jelonek, Fernandes, Alexandre +3 · 1 citation
Mathematics · #Algebraic Geometry and Number Theory #Mathematics and Applications #Geometric and Algebraic Topology
paper · pdf · doi:10.48550/arxiv.2309.07078
We show that for every k≥ 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 ℙ1× ℙ2. As an application we give an example of three four dimensional real algebraic cones in ℝ8 with isolated singularity which are semi-algebraically and bi-Lipschitz equivalent but they have non-homeomorphic bases.