Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Convex RP^2 Structures and Cubic Differentials under Neck Separation   Let S be a closed oriented surface of genus at least two. Labourie and the
author have independently used the theory of hyperbolic affine spheres to find
a natural correspondence between convex RP^2 structures on S and pairs
(\Sigma,U) consisting of a conformal structure \Sigma on S and a holomorphic
cubic differential U over \Sigma. The pairs (\Sigma,U$, for \Sigma varying in
moduli space, allow us to define natural holomorphic coordinates on the moduli
space of convex RP^2 structures. We consider geometric limits of convex RP^2
structures on S in which the RP^2 structure degenerates only along a set of
simple, non-intersecting, non-homotopic loops c. We classify the resulting RP^2
structures on S-c and call them regular convex RP^2 structures. We put a
natural topology on the moduli space of all regular convex RP^2 structures on S
and show that this space is naturally homeomorphic to the total space of the
vector bundle over the Deligne-Mumford compactification of the moduli space of
curves each of whose fibers over a noded Riemann surface is the space of
regular cubic differentials. In other words, we can extend our holomorphic
coordinates to bordify the moduli space of convex RP^2 structures along all
neck pinches. The proof relies on previous techniques of the author,
Benoist-Hulin, and Dumas-Wolf, as well as some details due to Wolpert of the
geometry of hyperbolic metrics on conformal surfaces in the Deligne-Mumford
compactification.

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The categories of this paper are: alg-geom
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The categories of this paper are: q-fin
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The categories of this paper are: gr-qc
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The categories of this paper are: acc-phys
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The categories of this paper are: chao-dyn
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The categories of this paper are: cmp-lg
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The categories of this paper are: hep-th
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The categories of this paper are: solv-int
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org
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The categories of this paper are: math-ph
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The categories of this paper are: q-alg
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The categories of this paper are: nucl-th
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The categories of this paper are: nucl-ex