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June 2019 A Note on Tropical Curves and the Newton Diagrams of Plane Curve Singularities
Takuhiro TAKAHASHI
Tokyo J. Math. 42(1): 51-61 (June 2019). DOI: 10.3836/tjm/1502179251

Abstract

For an isolated singularity which is Newton non-degenerate and also convenient, the Milnor number can be computed from the complement of its Newton diagram in the first quadrant by using Kouchnirenko's formula. In this paper, we consider tropical curves dual to subdivisions of this complement for a plane curve singularity, and show that there exists a tropical curve by which we can count the Milnor number. Our formula may be regarded as a tropical version of the well-known formula by the real morsification due to A'Campo and Gusein-Zade.

Citation

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Takuhiro TAKAHASHI. "A Note on Tropical Curves and the Newton Diagrams of Plane Curve Singularities." Tokyo J. Math. 42 (1) 51 - 61, June 2019. https://doi.org/10.3836/tjm/1502179251

Information

Published: June 2019
First available in Project Euclid: 18 July 2019

zbMATH: 07114900
MathSciNet: MR3982049
Digital Object Identifier: 10.3836/tjm/1502179251

Subjects:
Primary: 14T05
Secondary: 14B05, 52B20

Rights: Copyright © 2019 Publication Committee for the Tokyo Journal of Mathematics

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Vol.42 • No. 1 • June 2019
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