Tropical Moduli Space of Rational Graphically Stable Curves
Andy Fry
TL;DR
This paper explores the structure of moduli spaces of rational graphically stable tropical curves, revealing their fan structure aligns with the Bergman fan of the cycle matroid of a complete multipartite graph.
Contribution
It establishes that the moduli space of radially aligned -stable tropical curves forms a balanced fan identical to the Bergman fan of the cycle matroid of the graph.
Findings
The moduli space has a balanced fan structure.
The fan coincides with the Bergman fan of the cycle matroid.
Provides a combinatorial description of tropical moduli spaces.
Abstract
We study moduli spaces of rational graphically stable tropical curves and a refinement given by radial alignment. Given a complete multipartite graph , the moduli space of radially aligned -stable tropical curves can be given the structure of a balanced fan. This fan structure coincides with the Bergman fan of the cycle matroid of .
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Taxonomy
TopicsPolynomial and algebraic computation · Algebraic Geometry and Number Theory · Nonlinear Waves and Solitons