A-Tint: A polymake extension for algorithmic tropical intersection theory

Abstract

In this paper we study algorithmic aspects of tropical intersection theory. We analyse how divisors and intersection products on tropical cycles can actually be computed using polyhedral geometry. The main focus of this paper is the study of moduli spaces, where the underlying combinatorics of the varieties involved allow a much more efficient way of computing certain tropical cycles. The algorithms discussed here have been implemented in an extension for polymake, a software for polyhedral computations.

32 pages, 5 figures, 4 tables. Second version: Revised version, to be published in European Journal of Combinatorics

References in corpus (8)

• Matroid polytopes, nested sets and Bergman fans
• Moduli spaces of rational tropical curves
• The diagonal of tropical matroid varieties and cycle intersections
• Stable Intersections of Tropical Varieties
• Computing Tropical Linear Spaces
• Lifting representations of finite reductive groups I: Semisimple conjugacy classes
• Intersecting Psi-classes on tropical M_{0,n}
• A tropical intersection product in matroidal fans

Cited by in corpus (8)

• Stable Intersections of Tropical Varieties
• The intersection ring of matroids
• Algorithms for Tight Spans and Tropical Linear Spaces
• The Schläfli Fan
• Current Challenges in Developing Open Source Computer Algebra Systems
• On realizability of lines on tropical cubic surfaces and the Brundu-Logar normal form
• Tropical $\psi$ classes
• Combinatorics of tropical Hurwitz cycles