On K\"ahler conformal compactifications of $U(n)$-invariant ALE spaces

Michael G. Dabkowski; Michael T. Lock

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arXiv · 1405.4920

On K\"ahler conformal compactifications of $U(n)$-invariant ALE spaces

Michael G. Dabkowski·Michael T. Lock

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Abstract

We prove that a certain class of ALE spaces always has a Kahler conformal compactification, and moreover provide explicit formulas for the conformal factor and the Kahler potential of said compactification. We then apply this to give a new and simple construction of the canonical Bochner-K\"ahler metric on certain weighted projective spaces, and also to explicitly construct a family Kahler edge-cone metrics on $\mathbb{CP}^2$, with singular set $\mathbb{CP}^1$, having cone angles $2\pi\beta$ for all $\beta>0$. We conclude by discussing how these results can be used to obtain certain well-known Einstein metrics.

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BibTeX RIS

Michael G. Dabkowski, Michael T. Lock. 2014-05-19. On K\"ahler conformal compactifications of $U(n)$-invariant ALE spaces. https://arxiv.org/abs/1405.4920

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