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Obstructions to Approximating Tropical Curves in Surfaces Via Intersection Theory

Published online by Cambridge University Press:  20 November 2018

Erwan Brugallé  and
Kristin Shaw
Erwan Brugallé
Affiliation:
École polytechnique, Centre Mathématiques Laurent Schwatrz, 91 128 Palaiseau Cedex, France e-mail: erwan.brugalle@math.cnrs.fr
Kristin Shaw
Affiliation:
Department of Mathematics, University of Toronto, Toronto, ON, M5S 2E4 e-mail: shawkm@math.toronto.edu
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Abstract

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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.

Keywords

14T0514M25tropical geometryamoebasapproximation of tropical varietiesintersection theory

Information

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 67 , Issue 3 , 01 June 2015 , pp. 527 - 572
Copyright
Copyright © Canadian Mathematical Society 2015

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