ALE spaces and nodal curves

Nigel Hitchin

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arXiv · 2402.04021

ALE spaces and nodal curves

Nigel Hitchin

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Abstract

We consider the twistor theory approach to Kronheimer's ALE metrics on resolutions of the quotient of C^2 by a finite subgroup of SU(2). The circle action on the 4-manifold induces a C^* action on a compactification of the twistor space and we identify the orbit of a generic twistor line as a nodal rational curve in a particular cohomology class of a projective rational surface. Using the results of N.Honda et al we identify this surface with the minitwistor space for the Einstein-Weyl structure on the 3-dimensional quotient of the ALE space by the circle action.

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BibTeX RIS

Nigel Hitchin. 2024-02-06. ALE spaces and nodal curves. https://arxiv.org/abs/2402.04021

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