Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Principal bundles on projective varieties and the Donaldson-Uhlenbeck
  compactification   Let $H$ be a semisimple algebraic group. We prove the semistable reduction
theorem for $\mu$--semistable principal $H$--bundles over a {\it smooth
projective variety $X$} defined over the field $\bc$. When $X$ is a {\it smooth
projective surface} and $H$ is simple, we construct the algebro--geometric
Donaldson--Uhlenbeck compactification of the moduli space of $\mu$--semistable
principal $H$--bundles with fixed characteristic classes and describe its
points. For large characteristic classes we show that the moduli space of
$\mu$--stable principal $H$--bundles is non--empty.

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The categories of this paper are: bayes-an
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The categories of this paper are: q-fin
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The categories of this paper are: chao-dyn
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The categories of this paper are: atom-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: q-alg
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The categories of this paper are: nlin
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The categories of this paper are: cond-mat
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The categories of this paper are: hep-lat
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The categories of this paper are: supr-con
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The categories of this paper are: plasm-ph
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The categories of this paper are: econ
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The categories of this paper are: quant-ph
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The categories of this paper are: mtrl-th
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The categories of this paper are: nucl-th
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The categories of this paper are: alg-geom