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arXiv · 1403.0548

Tropical Images of Intersection Points

Ralph Morrison
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Abstract

A key issue in tropical geometry is the lifting of intersection points to a non-Archimedean field. Here, we ask: Where can classical intersection points of planar curves tropicalize to? An answer should have two parts: first, identifying constraints on the images of classical intersections, and, second, showing that all tropical configurations satisfying these constraints can be achieved. This paper provides the first part: images of intersection points must be linearly equivalent to the stable tropical intersection by a suitable rational function. Several examples provide evidence for the conjecture that our constraints may suffice for part two.

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Ralph Morrison. 2014-03-03. Tropical Images of Intersection Points. https://arxiv.org/abs/1403.0548

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