Desingularizations of Conformally Kaehler, Einstein Orbifolds
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866918324969930752 |
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| author | LeBrun, Claude Ozuch, Tristan |
| author_facet | LeBrun, Claude Ozuch, Tristan |
| contents | Let {(M,g_i)} be a sequence of smooth compact oriented Einstein 4-manifolds of fixed Einstein constant $λ> 0$ 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2601_19215 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Desingularizations of Conformally Kaehler, Einstein Orbifolds LeBrun, Claude Ozuch, Tristan Differential Geometry 53C25 primary, 53C23, 53C55 secondary Let {(M,g_i)} be a sequence of smooth compact oriented Einstein 4-manifolds of fixed Einstein constant $λ> 0$ 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. |
| title | Desingularizations of Conformally Kaehler, Einstein Orbifolds |
| topic | Differential Geometry 53C25 primary, 53C23, 53C55 secondary |
| url | https://arxiv.org/abs/2601.19215 |