Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: The Kobayashi pseudometric on algebraic manifold and a canonical
  fibration   Given a compact complex manifold X of dimension n, we define a bimeromorphic
invariant $\kappa_+(X)$ as the maximum p for which there is a saturated line
subsheaf L of the sheaf of holomorphic p forms whose Kodaira dimension $\kappa
(L)$ equals p. We call X special if $\kappa_+(X)=0$. We give some evidence that
this condition characterizes X to have identically vanishing Kobayashi
pseudometric. We use the well-known construction of F. Campana to give, for
each projective X a canonical fibration $f: X\to Y$ holomorphic outside a
proper subvariety of Y and whose general fibers are special. We show that the
inherited orbifold structure on Y defined via the minimum multiplicity of those
of the components of each fiber does not admit positive dimensional special
sub-orbifolds through the general points of Y. We note that the Iitaka
fibration or any rationally connected fibration of X is a natural factor of f
and we show that this solves a general conjecture in Mori's classification
program of algebraic varieties, namely, that an algebraic variety is either of
general type, or (birationally) has a canonical fibration with positive
dimensional special type fibers that factors through the Iitaka and rationally
connected fibrations of X.

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The categories of this paper are: adap-org
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The categories of this paper are: gr-qc
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The categories of this paper are: plasm-ph
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The categories of this paper are: eess
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The categories of this paper are: supr-con
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The categories of this paper are: math-ph
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The categories of this paper are: cs
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The categories of this paper are: mtrl-th
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The categories of this paper are: nlin
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The categories of this paper are: hep-ex
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The categories of this paper are: econ
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The categories of this paper are: ao-sci
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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: atom-ph
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The categories of this paper are: quant-ph