Abstract
In this article we characterize the polynomial maps \(F:\mathbb {C}^n\rightarrow \mathbb {C}^n\) for which \(F^{-1}(0)\) is finite and their multiplicity \(\mu (F)\) is equal to \(n!\mathrm V_n(\widetilde{\Gamma }_{+}(F))\), where \(\widetilde{\Gamma }_{+}(F)\) 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.
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Communicated by A. Constantin.
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.
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Bivià-Ausina, C., Huarcaya, J.A.C. Polynomial maps with maximal multiplicity and the special closure. Monatsh Math 188, 413–429 (2019). https://doi.org/10.1007/s00605-018-1204-9
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DOI: https://doi.org/10.1007/s00605-018-1204-9