A guide to tropical modifications
arXiv:1509.03443 · doi:10.55630/serdica.2026.52.109-156
Abstract
This paper surveys {\it tropical modifications}, a notion that has become part of the folklore of tropical geometry. Tropical modifications are used in tropical intersection theory, tropical Hodge theory, and the study of singularities. They admit interpretations in several contexts, including hyperbolic geometry, Berkovich spaces, and non-standard analysis. The goal of the paper is to present several points of view, give references, and illustrate the usefulness of tropical modifications. We assume that the reader has already encountered tropical modifications and wants to understand them better. The paper also contains two new contributions: an obstruction to the realizability of non-transversal intersections and a tropical version of Weil's reciprocity law.
published version
References in corpus (10)
- Tropical Geometry and its applications
- Moduli spaces of rational tropical curves
- Lifting tropical intersections
- Brief introduction to tropical geometry
- Tropical approach to Nagata's conjecture in positive characteristic
- The Newton polygon of a planar singular curve and its subdivision
- Tropicalization of Del Pezzo Surfaces
- Using Tropical Degenerations For Proving The Nonexistence Of Certain Nets
- Tropical surfaces
- Tropical Embeddings of Metric Graphs