Tropicalization of 1-tacnodal curves on toric surfaces

Takuhiro Takahashi

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arXiv · 1709.00788

Tropicalization of 1-tacnodal curves on toric surfaces

Takuhiro Takahashi

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Abstract

A degeneration of a singular curve on a toric surface, called a tropicalization, was constructed by E. Shustin. He classified the degeneration of 1-cuspidal curves using polyhedral complexes called tropical curves. In this paper, we define a tropical version of a 1-tacnodal curve, that is, a curve having exactly one singular point whose topological type is $A_3$, and by applying the tropicalization method, we classify tropical curves which correspond to 1-tacnodal curves.

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Takuhiro Takahashi. 2017-09-04. Tropicalization of 1-tacnodal curves on toric surfaces. https://arxiv.org/abs/1709.00788

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