We provide some new local obstructions to
tropical curves in
smooth tropical surfaces. These obstructions are based on
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
in tropical projective 3-space contains finitely
many approximable tropical lines
it is of degree 3, and contains no approximable tropical lines if
it is of degree 4 or more.
tropical geometry, amoebas, approximation of tropical varieties, intersection theory
14T05 - Tropical geometry [See also 12K10, 14M25, 14N10, 52B20]
14M25 - Toric varieties, Newton polyhedra [See also 52B20]