Geometry of tropical moduli spaces and linkage of graphs

2010/01/31 by Lucia Caporaso · 33 citations
Computer Science · Mathematics · #Algebraic Geometry and Number Theory #Codimension #Combinatorics #Computer science #Discrete mathematics #Enhanced Data Rates for GSM Evolution #Genus #Geometric and Algebraic Topology #Geometry #Linkage (software) #Mathematics #Moduli #Moduli space #Physics #Polynomial and algebraic computation #Pure mathematics #Sequence (biology) #Tropical geometry #math.AG #math.CO #msc:05CXX #msc:14TXX

paper · pdf · doi:10.1016/j.jcta.2011.11.011

published in Journal of Combinatorial Theory Series A 119(3), 579-598 (Elsevier BV) · Final version incorporating the referees corrections

arxiv created 2011/11/09 · arxiv updated 2011/11/18 · openalex publication_date 2011/11/22 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/05

Abstract

We prove the following "linkage" theorem: two p-regular graphs of the same genus can be obtained from one another by a finite alternating sequence of one-edge-contractions; moreover this preserves 3-edge-connectivity. We use the linkage theorem to prove that various moduli spaces of tropical curves are connected through codimension one.

Citations

• Moduli spaces of rational tropical curves
• Combinatorics of the tropical Torelli map
• The irreducibility of the space of curves of given genus
• A presentation for the mapping class group of a closed orientable surface
• Tropical Geometry and its applications
• Enumerative tropical algebraic geometry in R2

Cited by

• Algebraic and tropical curves: comparing their moduli spaces
• Tropical Amplitudes