Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Compact Kaehler quotients of algebraic varieties and Geometric Invariant
  Theory   Given an action of a complex reductive Lie group G on a normal variety X, we
show that every analytically Zariski-open subset of X admitting an analytic
Hilbert quotient with projective quotient space is given as the set of
semistable points with respect to some G-linearised Weil divisor on X.
  Applying this result to Hamiltonian actions on algebraic varieties we prove
that semistability with respect to a momentum map is equivalent to
GIT-semistability in the sense of Mumford and Hausen. It follows that the
number of compact momentum map quotients of a given algebraic Hamiltonian
G-variety is finite. As further corollary we derive a projectivity criterion
for varieties with compact Kaehler quotient.
  Additionally, as a byproduct of our discussion we give an example of a
complete Kaehlerian non-projective algebraic surface, which may be of
independent interest.

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The categories of this paper are: q-alg
11
The categories of this paper are: hep-lat
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The categories of this paper are: chem-ph
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The categories of this paper are: eess
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The categories of this paper are: bayes-an
5
The categories of this paper are: gr-qc
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The categories of this paper are: adap-org
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The categories of this paper are: solv-int
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The categories of this paper are: hep-ex
3
The categories of this paper are: physics
7
The categories of this paper are: hep-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
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The categories of this paper are: patt-sol
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The categories of this paper are: cmp-lg