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arXiv · 2601.19215

Desingularizations of Conformally Kaehler, Einstein Orbifolds

Claude LeBrun·Tristan Ozuch
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Abstract

Let {(M,g_i)} be a sequence of smooth compact oriented Einstein 4-manifolds of fixed Einstein constant $\lambda > 0$ that Gromov-Hausdorff converges to a 4-dimensional Einstein orbifold X. Suppose, moreover, that the limit metric is Hermitian with respect to some complex structure on the limit orbifold X, that X has at least one singular point, and that every gravitational instanton that bubbles off from the sequence is anti-self-dual. Then, for all sufficiently large i, the given (M,g_i) are all Kaehler-Einstein. As a consequence, the limit orbifold X is also Kaehler-Einstein, and must in fact be one of the orbifold limits classified by Odaka, Spotti, and Sun.

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Claude LeBrun, Tristan Ozuch. 2026-01-27. Desingularizations of Conformally Kaehler, Einstein Orbifolds. https://arxiv.org/abs/2601.19215

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