Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Tropical Geometric Compactification of Moduli, II - $A_g$ case and
  holomorphic limits -   We compactify the classical moduli variety $A_g$ of principally polarized
abelian varieties of complex dimension $g$ by attaching the moduli of flat tori
of real dimensions at most $g$ in an explicit manner. Equivalently, we
explicitly determine the Gromov-Hausdorff limits of principally polarized
abelian varieties. This work is analogous to the first of our series (available
at arXiv:1406.7772v2), which compactified the moduli of curves by attaching the
moduli of metrized graphs.
  Then, we also explicitly specify the Gromov-Hausdorff limits along
holomorphic family of abelian varieties and show that they form special
non-trivial subsets of the whole boundary. We also do it for algebraic curves
case and observe a crucial difference with the case of abelian varieties.

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The categories of this paper are: q-fin
29
The categories of this paper are: funct-an
12
The categories of this paper are: nucl-th
33
The categories of this paper are: plasm-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: bayes-an
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The categories of this paper are: econ
4
The categories of this paper are: cond-mat
7
The categories of this paper are: hep-th
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The categories of this paper are: mtrl-th
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The categories of this paper are: eess
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The categories of this paper are: chem-ph
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The categories of this paper are: nucl-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: supr-con
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The categories of this paper are: chao-dyn