Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Scalar curvature and an infinite-dimensional hyperk\"ahler reduction   We discuss a natural extension of the K\"ahler reduction of Fujiki and
Donaldson, which realises the scalar curvature of K\"ahler metrics as a moment
map, to a hyperk\"ahler reduction. Our approach is based on an explicit
construction of hyperk\"ahler metrics due to Biquard and Gauduchon. This
extension is reminiscent of how one derives Hitchin's equations for harmonic
bundles, and yields real and complex moment map equations which deform the
constant scalar curvature K\"ahler (cscK) condition. In the special case of
complex curves we recover previous results of Donaldson. We focus on the case
of complex surfaces. In particular we show the existence of solutions to the
moment map equations on a class of ruled surfaces which do not admit cscK
metrics.

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The categories of this paper are: supr-con
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The categories of this paper are: bayes-an
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The categories of this paper are: hep-ph
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The categories of this paper are: plasm-ph
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The categories of this paper are: q-bio
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The categories of this paper are: ao-sci
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The categories of this paper are: math-ph
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The categories of this paper are: cmp-lg
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The categories of this paper are: funct-an
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The categories of this paper are: stat
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The categories of this paper are: nucl-th
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The categories of this paper are: patt-sol
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The categories of this paper are: chem-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: eess
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The categories of this paper are: quant-ph