Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Some remarks on conic degeneration and bending of Poincar\'e-Einstein
  metrics   Let $(M,g)$ be a compact K\"ahler-Einstein manifold with $c_1 > 0$. Denote by
$K\to M$ the canonical line-bundle, with total space $X$, and $X_0$ the
singular space obtained by blowing down $X$ along its zero section. We employ a
construction by Page and Pope and discuss an interesting multi-parameter family
of Poincar\'e--Einstein metrics on $X$. One 1-parameter subfamily
$\{g_t\}_{t>0}$ has the property that as $t\searrow 0$, $g_t$ converges to a PE
metric $g_0$ on $X_0$ with conic singularity, while $t^{-1}g_t$ converges to a
complete Ricci-flat K\"ahler metric $\hat{g}_0$ on $X$. Another 1-parameters
subfamily has an edge singularity along the zero section of $X$, with cone
angle depending on the parameter, but has constant conformal infinity. These
illustrate some unexpected features of the Poincar\'e-Einstein moduli space.

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The categories of this paper are: quant-ph
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The categories of this paper are: dg-ga
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The categories of this paper are: bayes-an
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The categories of this paper are: adap-org
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The categories of this paper are: cmp-lg
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The categories of this paper are: nlin
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The categories of this paper are: solv-int
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The categories of this paper are: gr-qc
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The categories of this paper are: funct-an
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The categories of this paper are: astro-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: chao-dyn
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The categories of this paper are: hep-lat
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The categories of this paper are: q-fin
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The categories of this paper are: hep-ph