English

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

Algebraic Geometry 2017-05-10 v2 Algebraic Topology Complex Variables

Abstract

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

Keywords

Cite

@article{arxiv.1702.06213,
  title  = {Multiplicity, regularity and blow-spherical equivalence of complex analytic sets},
  author = {J. Edson Sampaio},
  journal= {arXiv preprint arXiv:1702.06213},
  year   = {2017}
}

Comments

24 pages. New references have been added, some typos have been corrected and some details have been added in the proof of Theorem 5.18