Multiplicity, regularity and blow-spherical equivalence of complex analytic sets (Q2657842)

The paper studies multiplicity and regularity of complex analytic sets. It presents blow-spherical equivalence for such sets. Two subset germs of Euclidean spaces are blow-spherical equivalent, if their spherical modifications are homeomorphic and, in particular, this homeomorphism induces a homeomorphism between their tangent links. This equivalence lives between topological equivalence and subanalytic bi-Lipschitz equivalence. The author reduces the study of multiplicity and regularity to a version of Zariski's multiplicity conjecture in the case of blow-spherical homeomorphism and gives some partial answers to Zariski's multiplicity conjecture by showing that a blow-spherical regular complex analytic set is smooth and by giving a complete classification of complex analytic curves.