Tropical images of intersection points

• Autores: Ralph Morrison
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 66, Fasc. 2, 2015, págs. 273-283
• Idioma: inglés
• DOI: 10.1007/s13348-014-0118-7
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• Resumen

  • 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.