Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Extending Torelli map to toroidal compactifications of Siegel space   It has been known since the 1970s that the Torelli map $M_g \to A_g$,
associating to a smooth curve its jacobian, extends to a regular map from the
Deligne-Mumford compactification $\bar{M}_g$ to the 2nd Voronoi
compactification $\bar{A}_g^{vor}$.
  We prove that the extended Torelli map to the perfect cone (1st Voronoi)
compactification $\bar{A}_g^{perf}$ is also regular, and moreover
$\bar{A}_g^{vor}$ and $\bar{A}_g^{perf}$ share a common Zariski open
neighborhood of the image of $\bar{M}_g$. We also show that the map to the
Igusa monoidal transform (central cone compactification) is NOT regular for
$g\ge9$; this disproves a 1973 conjecture of Namikawa.

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The categories of this paper are: math-ph
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The categories of this paper are: hep-ex
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The categories of this paper are: dg-ga
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The categories of this paper are: hep-lat
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The categories of this paper are: cs
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The categories of this paper are: adap-org
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: hep-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: chem-ph
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The categories of this paper are: econ
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The categories of this paper are: acc-phys
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The categories of this paper are: cmp-lg
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The categories of this paper are: nucl-ex
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The categories of this paper are: cond-mat