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On the intersection multiplicity of plane branches. (English) Zbl 1434.32042

Summary: We prove an intersection formula for two plane branches in terms of their semigroups and key polynomials. Then we provide a strong version of Bayer’s theorem on the set of intersection multiplicities of two branches with fixed characteristics and apply it to the logarithmic distance in the space of branches.

MSC:

32S05 Local complex singularities
14H20 Singularities of curves, local rings
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References:

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[6] B. L. van der Waerden, Einführung in die algebraische Geometrie, Springer, Berlin, 1939. Evelia R. García Barroso Departamento de Matemáticas, Estadística e I.O. Sección de Matemáticas Universidad de La Laguna Apartado de Correos 456 38200 La Laguna, Tenerife, Spain E-mail: ergarcia@ull.es Arkadiusz Płoski Department of Mathematics and Physics Kielce University of Technology Al. Tysiąclecia Państwa Polskiego 7 25-314 Kielce, Poland E-mail: matap@tu.kielce.pl
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