Resumen de Tropical images of intersection points

Ralph Morrison

• 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.