Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: K\"ahler spaces with zero first Chern class: Bochner principle,
  fundamental groups, and the Kodaira problem   Let $X$ be a compact K\"ahler space with klt singularities and vanishing
first Chern class. We prove the Bochner principle for holomorphic tensors on
the smooth locus of $X$: any such tensor is parallel with respect to the
singular Ricci-flat metrics. As a consequence, after a finite quasi-\'etale
cover $X$ splits off a complex torus of the maximum possible dimension. We then
proceed to decompose the tangent sheaf of $X$ according to its holonomy
representation. In particular, we classify those $X$ which have strongly stable
tangent sheaf: up to quasi-\'etale covers, these are either Calabi-Yau or
irreducible holomorphic symplectic.
  Several applications of these results are given, the strongest ones of which
apply in dimension four. In this case, we prove Campana's Abelianity Conjecture
for $X$. If in addition $X$ has only algebraic singularities then a cover of
$X$ admits small projective deformations and the Beauville-Bogomolov
Decomposition Theorem holds for $X$.

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The categories of this paper are: q-bio
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The categories of this paper are: comp-gas
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The categories of this paper are: cmp-lg
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The categories of this paper are: physics
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The categories of this paper are: gr-qc
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The categories of this paper are: math-ph
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The categories of this paper are: hep-th
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The categories of this paper are: nucl-ex
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The categories of this paper are: hep-lat
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The categories of this paper are: hep-ph
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: quant-ph
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The categories of this paper are: stat
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The categories of this paper are: chem-ph
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The categories of this paper are: dg-ga