TL;DR
This paper investigates the geometry of the fixed point set of a circle action on an ALE space with a hyperkähler metric, linking it to algebraic geometry of rational curves on surfaces.
Contribution
It provides a detailed description of the induced metric on the fixed sphere using algebraic geometry, connecting hyperkähler geometry with rational curves.
Findings
Characterization of the fixed sphere as a rational curve
Description of the induced metric via algebraic geometry
Connection between hyperkähler metrics and algebraic surface theory
Abstract
This paper focuses on the spherical fixed point set of a circle action on an ALE space endowed with Kronheimer's hyperkaehler metric. The induced metric on the sphere is described by using the algebraic geometry of rational curves on algebraic surfaces, in particular the lines on a cubic.
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