Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tropical Igusa Invariants   Let $X$ be a smooth geometrically connected projective curve of genus two
over a complete non-archimedean field $K$. For discretely valued $K$, the first
main theorem in \cite{liu} gives a set of criteria on the Igusa invariants of
the curve that determine the minimal Berkovich skeleton of $X$ together with
its edge lengths and vertex weights. In this paper we use the theory of
Berkovich spaces to give a new proof of this theorem that works for arbitrary
complete non-archimedean fields. We furthermore interpret the final result in
terms of tropical moduli spaces and tropical Igusa invariants. This
reformulation shows that the abstract tropicalization map
${M}_{2}\to\mathrm{trop}(M_{2})$ factors through the tropicalization of a
concrete embedding of ${M}_{2}$ into a weighted projective space.

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The categories of this paper are: physics
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The categories of this paper are: patt-sol
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The categories of this paper are: chao-dyn
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: gr-qc
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: solv-int
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The categories of this paper are: astro-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: supr-con
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The categories of this paper are: quant-ph
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The categories of this paper are: nucl-th
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The categories of this paper are: q-alg