Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Orbifold resolution via hyperkahler quotients: the $D_2$ ALF manifold   We propose an infinite-dimensional generalization of Kronheimer's
construction of families of hyperkahler manifolds resolving flat orbifold
quotients of $\mathbb{R}^4$. As in [Kro89], these manifolds are constructed as
hyperkahler quotients of affine spaces. This leads to a study of \emph{singular
equivariant instantons} in various dimensions. In this paper, we study singular
equivariant Nahm data to produce the family of $D_2$ asymptotically locally
flat (ALF) manifolds as a deformation of the flat orbifold $(\mathbb{R}^3
\times S^1)/Z_2$. We furthermore introduce a notion of stability for Nahm data
and prove a Donaldson-Uhlenbeck-Yau type theorem to relate real and complex
formulations. We use these results to construct a canonical Ehresmann
connection on the family of non-singular $D_2$ ALF manifolds. In the complex
formulation, we exhibit explicit relationships between these $D_2$ ALF
manifolds and corresponding $A_1$ ALE manifolds. We conjecture analogous
constructions and results for general orbifold quotients of $\mathbb{R}^{4-r}
\times T^r$ with $2 \le r \le 4$. The case $r = 4$ produces K3 manifolds as
hyperkahler quotients.

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The categories of this paper are: nucl-th
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The categories of this paper are: cond-mat
34
The categories of this paper are: chem-ph
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The categories of this paper are: q-bio
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The categories of this paper are: stat
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The categories of this paper are: acc-phys
35
The categories of this paper are: mtrl-th
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The categories of this paper are: funct-an
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The categories of this paper are: q-alg
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The categories of this paper are: eess
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The categories of this paper are: math-ph
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The categories of this paper are: econ
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The categories of this paper are: nlin
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The categories of this paper are: plasm-ph
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The categories of this paper are: adap-org
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The categories of this paper are: astro-ph