ALE spaces and nodal curves
Differential Geometry
2024-02-07 v1
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.
Cite
@article{arxiv.2402.04021,
title = {ALE spaces and nodal curves},
author = {Nigel Hitchin},
journal= {arXiv preprint arXiv:2402.04021},
year = {2024}
}
Comments
Based on a talk given at a conference in Oxford for Peter Kronheimer's 60th birthday in July 2023