An index theorem on anti-self-dual orbifolds

2012/02/02 by Viaclovsky, Jeff A.
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics

paper · doi:10.48550/arxiv.1202.0578

Abstract

An index theorem for the anti-self-dual deformation complex on anti-self-dual orbifolds with singularities conjugate to ADE-type is proved. In 1988, Claude Lebrun gave examples of scalar-flat Kähler ALE metrics with negative mass, on the total space of the bundle O(-n) over S². A corollary of this index theorem is that the moduli space of anti-self-dual ALE metrics near each of these metrics has dimension at least 4n-12, and thus for n ≥ 4 the LeBrun metrics admit a plethora of non-trivial anti-self-dual deformations.

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