Polynomial maps with maximal multiplicity and the special closure

Carles Bivià-Ausina, Jorge A.C. Huarcaya

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In this article we characterize the polynomial maps F: C n → C n for which F - 1 (0) is finite and their multiplicity μ(F) is equal to n! V n (Γ ~ + (F)) , where Γ ~ + (F) is the global Newton polyhedron of F. As an application, we derive a characterization of those polynomial maps whose multiplicity is maximal with respect to a fixed Newton filtration.

Original languageEnglish
Pages (from-to)413-429
Number of pages17
JournalMonatshefte fur Mathematik
Issue number3
StatePublished - 11 Mar 2019

Bibliographical note

Funding Information:
Carles Bivià-Ausina was partially supported by DGICYT Grant MTM2015-64013-P. Jorge A. C. Huarcaya was partially supported by FAPESP-BEPE 2012/22365–8.

Publisher Copyright:
© 2018, Springer-Verlag GmbH Austria, part of Springer Nature.


  • Complex polynomial maps
  • Milnor number
  • Multiplicity
  • Newton polyhedron


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