Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Combinatorics of the tropical Torelli map   This paper is a combinatorial and computational study of the moduli space of
tropical curves of genus g, the moduli space of principally polarized tropical
abelian varieties, and the tropical Torelli map. These objects were introduced
recently by Brannetti, Melo, and Viviani. Here, we give a new definition of the
category of stacky fans, of which the aforementioned moduli spaces are objects
and the Torelli map is a morphism. We compute the poset of cells of tropical
M_g and of the tropical Schottky locus for genus at most 5. We show that
tropical A_g is Hausdorff, and we also construct a finite-index cover for A_3
which satisfies a tropical-type balancing condition. Many different
combinatorial objects, including regular matroids, positive semidefinite forms,
and metric graphs, play a role.

22
The categories of this paper are: chao-dyn
23
The categories of this paper are: solv-int
5
The categories of this paper are: gr-qc
37
The categories of this paper are: supr-con
13
The categories of this paper are: quant-ph
6
The categories of this paper are: astro-ph
25
The categories of this paper are: patt-sol
30
The categories of this paper are: q-alg
31
The categories of this paper are: ao-sci
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The categories of this paper are: comp-gas
1
The categories of this paper are: cs
8
The categories of this paper are: hep-ex
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The categories of this paper are: hep-lat
20
The categories of this paper are: acc-phys
29
The categories of this paper are: funct-an
33
The categories of this paper are: plasm-ph