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On the intersection multiplicity of plane branches

Volume 156 / 2019

Evelia R. García Barroso, Arkadiusz Płoski Colloquium Mathematicum 156 (2019), 243-254 MSC: Primary 32S05; Secondary 14H20. DOI: 10.4064/cm7444-4-2018 Published online: 24 January 2019


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.


  • Evelia R. García BarrosoDepartamento de Matemáticas,
    Estadística e I.O.
    Sección de Matemáticas
    Universidad de La Laguna
    Apartado de Correos 456
    38200 La Laguna, Tenerife, Spain
  • Arkadiusz PłoskiDepartment of Mathematics and Physics
    Kielce University of Technology
    Al. Tysiąclecia Państwa Polskiego 7
    25-314 Kielce, Poland

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