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Anti-holonomic jets and the Lie bracket

Michal Krupka (1998)

Archivum Mathematicum

Second order anti-holonomic jets as anti-symmetric parts of second order semi-holonomic jets are introduced. The anti-holonomic nature of the Lie bracket is shown. A general result on universality of the Lie bracket is proved.

Anti-self-dual orbifolds with cyclic quotient singularities

Michael T. Lock, Jeff A. Viaclovsky (2015)

Journal of the European Mathematical Society

An index theorem for the anti-self-dual deformation complex on anti-self-dual orbifolds with cyclic quotient singularities is proved. We present two applications of this theorem. The first is to compute the dimension of the deformation space of the Calderbank–Singer scalar-flat Kähler toric ALE spaces. A corollary of this is that, except for the Eguchi–Hanson metric, all of these spaces admit non-toric anti-self-dual deformations, thus yielding many new examples of anti-self-dual ALE spaces. For...

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