A proof of the differentiable invariance of the multiplicity using spherical blowing-up

In this paper we use some properties of spherical blowing-up to give an alternative and more geometric proof of Gau–Lipman Theorem about the differentiable invariance of the multiplicity of complex analytic sets. Moreover, we also provide a generalization of the Ephraim–Trotman Theorem.

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Bibliographische Detailangaben
Veröffentlicht in:	Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2019-10, Vol.113 (4), p.3913-3920
1. Verfasser:	Sampaio, J. Edson
Format:	Artikel
Sprache:	eng
Schlagworte:	Applications of Mathematics Blowing Invariance Mathematical and Computational Physics Mathematics Mathematics and Statistics Original Paper Theorems Theoretical
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Beschreibung
Zusammenfassung:	In this paper we use some properties of spherical blowing-up to give an alternative and more geometric proof of Gau–Lipman Theorem about the differentiable invariance of the multiplicity of complex analytic sets. Moreover, we also provide a generalization of the Ephraim–Trotman Theorem.
ISSN:	1578-7303 1579-1505
DOI:	10.1007/s13398-018-0537-5