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arXiv · 1202.0578

An index theorem on anti-self-dual orbifolds

Jeff A. Viaclovsky
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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 $\mathcal{O}(-n)$ over $S^2$. 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 $n \geq 4$ the LeBrun metrics admit a plethora of non-trivial anti-self-dual deformations.

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Jeff A. Viaclovsky. 2013-04-19. An index theorem on anti-self-dual orbifolds. https://arxiv.org/abs/1202.0578

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