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

摘要

This paper is devoted to study multiplicity and regularity as well as topresent some classifications of complex analytic sets. We present anequivalence for complex analytical sets, namely blow-spherical equivalence andwe receive several applications with this new approach. For example, we reduceto homogeneous complex algebraic sets a version of Zariski's multiplicityconjecture in the case of blow-spherical homeomorphism, we give some partialanswers to the Zariski's multiplicity conjecture, we show that a blow-sphericalregular complex analytic set is smooth and we give a complete classification ofcomplex analytic curves.