Moduli of algebraic and tropical curves
Dan Abramovich
TL;DR
This paper provides an accessible overview of the moduli spaces of algebraic and tropical curves, exploring their combinatorial structures, compactifications, and connections via non-archimedean geometry.
Contribution
It offers a non-technical exposition linking algebraic and tropical moduli spaces, highlighting their combinatorial and geometric relationships.
Findings
Descriptions of moduli spaces of algebraic and tropical curves
Connections between non-archimedean geometry and moduli theory
Insights into the combinatorics of compactifications
Abstract
This is mostly* a non-technical exposition of the joint work arXiv:1212.0373 with Caporaso and Payne. Topics include: Moduli of Riemann surfaces / algebraic curves; Deligne-Mumford compactification; Dual graphs and the combinatorics of the compactification; Tropical curves and their moduli; Non-archimedean geometry and comparison. * Maybe the last section is technical.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Polynomial and algebraic computation · Commutative Algebra and Its Applications