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.Comment: 13 pages. arXiv admin note: text overlap with arXiv:2302.0538