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Asian Journal of Mathematics
Volume 24 (2020)
Multiplicity, regularity and blow-spherical equivalence of complex analytic sets
Pages: 803 – 820
This paper is devoted to study multiplicity and regularity of complex analytic sets. We present an equivalence for complex analytical sets, named blow-spherical equivalence and we obtain 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 the complex analytic curves.
regularity, blow-spherical equivalence, complex analytic sets
2010 Mathematics Subject Classification
14B05, 32S05, 32S50
The author was partially supported by CNPq-Brazil grant 303811/2018-8, by the ERCEA 615655 NMST Consolidator Grant and also by the Basque Government through the BERC 2018-2021 program and Gobierno Vasco Grant IT1094-16, by the Spanish Ministry of Science, Innovation and Universities: BCAM Severo Ochoa accreditation SEV-2017-0718.
Received 22 July 2017
Accepted 29 January 2020
Published 10 March 2021