Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Elliptic constructions of hyperkaehler metrics I: The Atiyah-Hitchin
  manifold   This is the first in a series of papers in which we develop a twistor-based
method of constructing hyperkaehler metrics from holomorphic functions and
elliptic curves. As an application, we revisit the Atiyah-Hitchin manifold and
derive in an explicit holomorphic coordinate basis closed-form formulas for,
among other things, the metric, the holomorphic symplectic form and all three
Kaehler potentials.

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The categories of this paper are: alg-geom
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The categories of this paper are: adap-org
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The categories of this paper are: q-alg
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The categories of this paper are: bayes-an
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The categories of this paper are: mtrl-th
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The categories of this paper are: plasm-ph
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The categories of this paper are: quant-ph
11
The categories of this paper are: hep-lat
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The categories of this paper are: econ
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The categories of this paper are: nucl-ex
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The categories of this paper are: funct-an
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The categories of this paper are: math-ph
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The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
3
The categories of this paper are: physics
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The categories of this paper are: comp-gas