Moduli Spaces of Rational Graphically Stable Curves
Andy Fry
TL;DR
This paper introduces a new stability condition for algebraic moduli spaces of rational curves using graph theory, and characterizes when tropical compactifications align with geometric tropicalization, specifically for complete multipartite graphs.
Contribution
It defines a novel stability condition based on graphs and characterizes the cases where tropical and algebraic compactifications coincide, focusing on complete multipartite graphs.
Findings
Tropical compactification matches geometric tropicalization only for complete multipartite graphs.
A new graph-based stability condition for rational curves is established.
Characterization of when tropical and algebraic moduli spaces agree.
Abstract
We use a graph to define a new stability condition for algebraic moduli spaces of rational curves. We characterize when the tropical compactification of the moduli space agrees with the theory of geometric tropicalization. The characterization statement occurs only when the graph is complete multipartite.
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Taxonomy
TopicsPolynomial and algebraic computation · Spinal Hematomas and Complications