Obstructions to Approximating Tropical Curves in Surfaces Via Intersection Theory

Brugallé, Erwan ; Shaw, Kristin

Canadian journal of mathematics, Tome 67 (2015) no. 3, pp. 527-572

Résumé

We provide some new local obstructions to approximating tropical curves in smooth tropical surfaces. These obstructions are based on a relation between tropical and complex intersection theories, which is also established here. We give two applications of the methods developed in this paper. First we classify all locally irreducible approximable 3-valent fan tropical curves in a fan tropical plane. Secondly, we prove that a generic non-singular tropical surface in tropical projective 3-space contains finitely many approximable tropical lines if it is of degree 3, and contains no approximable tropical lines if it is of degree 4 or more.

Détail

DOI : 10.4153/CJM-2014-014-4

Mots-clés : 14T05, 14M25, tropical geometry, amoebas, approximation of tropical varieties, intersection theory

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