6 papers
Level structures on tropical abelian varieties
Eran Assaf, Madeline Brandt, Juliette Bruce +2
We introduce level structures on tropical abelian varieties and give a modular interpretation of , the tropicalization of the moduli space $\mathcal{A}_g[m]…
Tropical elliptic curves in 3-space
Laura Casabella, Lars Kastner, Raluca Vlad
We classify trivalent graphs with 16 vertices and 16 edges that arise from intersecting two quadratic surfaces in tropical 3-space. There are 4,009 such graphs, representing maxima…
Tropicalizations of locally symmetric varieties
Eran Assaf, Madeline Brandt, Juliette Bruce +2
This paper provides a rigorous study of tropicalizations of locally symmetric varieties. We give applications beyond tropical geometry, to the cohomology of moduli spaces as well a…
Maximal Mumford Curves from Planar Graphs
Mario Kummer, Bernd Sturmfels, Raluca Vlad
A curve of genus g is maximal Mumford (MM) if it has g+1 ovals and g tropical cycles. We construct full-dimensional families of MM curves in the Hilbert scheme of canonical curves.…
Graph Curve Matroids
Alheydis Geiger, Kevin Kuehn, Raluca Vlad
We introduce a new class of matroids, called graph curve matroids. A graph curve matroid is associated to a graph and defined on the vertices of the graph as a ground set. We prove…
Moduli dimensions of lattice polygons
Marino Echavarria, Max Everett, Shinyu Huang +5
Given a lattice polygon with interior lattice points, we associate to it the moduli space of tropical curves of genus with Newton polygon . We completely classify th…