Harmonic metrics on Higgs sheaves and uniformization of varieties of general type
Harmonic metrics on Higgs sheaves and uniformization of varieties of general type
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DOI：
10.1007/s00208-019-01906-4
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发表时间：
2018-04
影响因子：
1.4
通讯作者：
D. Greb;Stefan Kebekus;T. Peternell;Behrouz Taji
中科院分区：
文献类型：
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作者：
D. Greb;Stefan Kebekus;T. Peternell;Behrouz Taji
我们证明了一个标准的希格斯丛上定义的光滑轨迹的klt品种的调和度量的存在。作为一个应用程序，我们解决了准-étale均匀化问题的最小品种的一般类型，以获得一个完整的数值特征的奇异子的单位球的离散，co-compact群的自同构，自由地在余维1。作为进一步的应用，我们建立了klt变种光滑位点上的非交换Hodge对应。
We prove a criterion for the existence of harmonic metrics on Higgs bundles that are defined on smooth loci of klt varieties. As one application, we resolve the quasi-étale uniformisation problem for minimal varieties of general type to obtain a complete numerical characterisation of singular quotients of the unit ball by discrete, co-compact groups of automorphisms that act freely in codimension one. As a further application, we establish a nonabelian Hodge correspondence on smooth loci of klt varieties.