论文标题
爱因斯坦指标降低的高阶障碍
Higher order obstructions to the desingularization of Einstein metrics
论文作者
论文摘要
我们发现，通过平滑的爱因斯坦指标，紧凑的爱因斯坦奥比菲尔德的降低障碍。这些新的障碍（特定于紧凑型情况）提出了一个问题，即紧凑的爱因斯坦$ 4 $ -ORBIFOLD是否是爱因斯坦指标的限制，燃烧Eguchi-Hanson指标必须是Kähler。然后，我们测试这些障碍物，以讨论是否有可能通过1981年Page提出的最有前途的降值配置来产生Ricci-flat，但不能产生Kähler指标。我们确定了$ 84 $的障碍物，曾经与57美元的自由度相比，几乎所有的自由度相比，几乎所有的flat flat olbifold cornive of $ \ z^y Mathbb}是带有通用全能的RICCI-FLAT指标的限制，同时冒出Eguchi-Hanson指标。也许令人惊讶的是，在最对称的情况下，我们还确定了满足我们所有$ 84 $障碍的底线化的$ 14 $维度家族。
We find new obstructions to the desingularization of compact Einstein orbifolds by smooth Einstein metrics. These new obstructions, specific to the compact situation, raise the question of whether a compact Einstein $4$-orbifold which is limit of Einstein metrics bubbling out Eguchi-Hanson metrics has to be Kähler. We then test these obstructions to discuss if it is possible to produce a Ricci-flat but not Kähler metric by the most promising desingularization configuration proposed by Page in 1981. We identify $84$ obstructions which, once compared to the $57$ degrees of freedom, indicate that almost all flat orbifold metrics on $\mathbb{T}^4/\mathbb{Z}_2$ should not be limit of Ricci-flat metrics with generic holonomy while bubbling out Eguchi-Hanson metrics. Perhaps surprisingly, in the most symmetric situation, we also identify a $14$-dimensional family of desingularizations satisfying all of our $84$ obstructions.
