基于四元数复化的标量平坦Kähler轨道折叠
Scalar-flat Kähler orbifolds via quaternionic-complex reduction
摘要：
本文证明了：任何等距群包含2-环面的渐近局部欧氏标量平坦Kähler 4-orbifold，直到一个orbifold覆盖，都等距于一个$k$ -维四元数向量空间被一个$(k-1)$ -环面的四元数复商.为了做到这一点，我们首先证明了任何具有正欧拉示性数的紧致反自对偶4-orbifold，其等距群包含一个2-torus，是共形等价的，直到一个orbifold覆盖，$k$ -维四元数射影空间的四元数商的$(k-1)$ -torus。
英文摘要：
We prove that any asymptotically locally Euclidean scalar-flat Kähler 4-orbifold whose isometry group contains a 2-torus is isometric, up to an orbifold covering, to a quaternionic-complex quotient of a $k$-dimensional quaternionic vector space by a $(k-1)$-torus. In order to do so, we first prove that any compact anti-self-dual 4-orbifold with positive Euler characteristic whose isometry group contains a 2-torus is conformally equivalent, up to an orbifold covering, to a quaternionic quotient of $k$-dimensional quaternionic projective space by a $(k-1)$-torus.
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