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arXiv · 1607.05503

A note on tropical curves and the Newton diagrams of plane curve singularities

Takuhiro Takahashi
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Abstract

For a convenient and Newton non-degenerate singularity, the Milnor number is computed from the complement of its Newton diagram in the first quadrant, so-called Kouchnirenko's formula. In this paper, we consider tropical curves dual to subdivisions of this complement for a plane curve singularity and show the existence of a tropical curve satisfying a certain formula, which looks like a well-known formula for a real morsification due to A'Campo and Gusein-Zade.

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Takuhiro Takahashi. 2016-07-19. A note on tropical curves and the Newton diagrams of plane curve singularities. https://arxiv.org/abs/1607.05503

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