Algebraic and tropical curves: comparing their moduli spaces

Abstract

We construct the moduli space for equivalence classes of n-pointed tropical curves of genus g, together with its compactification given by weighted tropical curves, and establish some of its basic topological properties. We compare it to the moduli spaces of smooth and stable algebraic curves, from the combinatorial, the topological, and the Teichmüller point of view. The paper is written in an expository style, and it generalizes some results contained in sections 4-6 of arXiv:1001.2815v3.

Changes in numbering to match the published version

References in corpus (5)

• On the tropical Torelli map
• Moduli spaces of rational tropical curves
• Geometry of tropical moduli spaces and linkage of graphs
• Riemann-Roch theory for weighted graphs and tropical curves
• A tropical proof of the Brill-Noether Theorem

Cited by in corpus (18)

• Tropical curves, graph complexes, and top weight cohomology of M_g
• Tropical Amplitudes
• Geometry of tropical moduli spaces and linkage of graphs
• The universal tropical Jacobian and the skeleton of the Esteves' universal Jacobian
• A note on Brill-Noether thoery and rank determining sets for metric graphs
• Riemann-Roch theory for weighted graphs and tropical curves
• Moduli spaces of colored graphs
• Tropical geometry of genus two curves
• On the Riemann-Hurwitz formula for graph coverings
• Tropical curves and covers and their moduli spaces
• Maximal harmonic group actions on finite graphs
• A universal tropical Jacobian over $M_g^{\trop}$
• The Moduli Space of Harnack Curves in Toric Surfaces
• Tropical Geometric Compactification of Moduli, II - $A_g$ case and holomorphic limits -
• Complete invariant geodesic metrics on outer spaces and Jacobian varieties of tropical curves
• The tropical Manin-Mumford conjecture
• Schottky spaces and universal Mumford curves over $\mathbb{Z}$
• Connectedness of the Moduli Space of Genus 1 Planar Tropical Curves