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Moduli spaces of rational graphically stable curves

Date

2021

Authors

Fry, Andy J., author
Cavalieri, Renzo, advisor
Shoemaker, Mark, committee member
Wilson, James, committee member
Tavani, Daniele, committee member

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Abstract

We use a graph to define a new stability condition for the algebraic and tropical moduli spaces of rational curves. Tropically, we characterize when the moduli space has the structure of a balanced fan by proving a combinatorial bijection between graphically stable tropical curves and chains of flats of a graphic matroid. Algebraically, we characterize when the tropical compactification of the compact moduli space agrees with the theory of geometric tropicalization. Both characterization results occur only when the graph is complete multipartite.

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