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arXiv 2012.148952020-12math.DGhep-thmath.AG

Deformations of hyperkähler cones

Roger Bielawski, Lorenzo Foscolo

备注：: v3: revisions to the introduction and to the presentation of Section 3 to emphasise the application to hyperkähler quotients

英文摘要：

We use twistor methods to promote Namikawa's universal Poisson deformations of conic affine symplectic singularities to families of hyperkähler structures deforming hyperkähler cone metrics. The metrics we produce are generally incomplete, but for specific classes of hyperkähler cones, even these incomplete metrics have some interest and applications: we study in detail the case of the nilpotent cone of a simple complex Lie algebra, with applications to hyperkähler metrics with symmetries and hyperkähler quotients, and the case of Kleinian singularities, with applications to codimension-4 singularities of G2-holonomy metrics and their dual description in theoretical physics in terms of 3-dimensional gauge theory.

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