Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Transversely holomorphic branched Cartan geometry   Earlier we introduced and studied the concept of holomorphic {\it branched
Cartan geometry}. We define here a foliated version of this notion; this is
done in terms of Atiyah bundle. We show that any complex compact manifold of
algebraic dimension $d$ admits, away from a closed analytic subset of positive
codimension, a nonsingular holomorphic foliation of complex codimension $d$
endowed with a transversely flat branched complex projective geometry
(equivalently, a ${\mathbb C}P^d$-geometry). We also prove that transversely
branched holomorphic Cartan geometries on compact complex projective rationally
connected varieties and on compact simply connected Calabi-Yau manifolds are
always flat (consequently, they are defined by holomorphic maps into
homogeneous spaces).

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The categories of this paper are: econ
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The categories of this paper are: plasm-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: stat
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The categories of this paper are: quant-ph
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The categories of this paper are: cond-mat
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The categories of this paper are: comp-gas
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The categories of this paper are: q-fin
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The categories of this paper are: cmp-lg
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The categories of this paper are: chao-dyn
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The categories of this paper are: physics
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The categories of this paper are: astro-ph
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The categories of this paper are: q-alg
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The categories of this paper are: solv-int
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The categories of this paper are: supr-con
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The categories of this paper are: nlin