发表机构
Tohoku University; East China Normal University（东北大学; 华东师范大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文从切层正性角度研究允许int-amplified自同态的紧致Kähler簇，证明其切层弱正弯曲，并建立Kähler版本的Yoshikawa结构定理，同时证明极小模型存在性及自同态提升性质。
AI 中文摘要
我们从切层的正性角度研究允许int-amplified自同态的紧致Kähler簇。我们的主要结果表明，此类簇的切层是弱正弯曲的；特别地，它在强意义上是伪有效的。这建立了复动力系统与切层正性理论之间的新联系，并为紧致Kähler环境中的等变MMP技术提供了一种替代方案。作为应用，我们证明了Yoshikawa结构定理的Kähler类比：对于允许int-amplified自同态的紧致Kähler klt簇，经过等变拟平展覆盖后，它允许一个等变的平坦MRC纤维化，其不可约纤维映射到复环面上；在光滑情形下，该纤维化是光滑的，其周期纤维为Fano型。为此，我们证明了在非射影Kähler簇中数值维数为零的典范除子情形下极小模型的存在性。我们进一步研究具有伪有效切丛的有理连通流形，重点关注它们与Fano型性质、几乎齐次性和基本群的关系。在证明中，我们还证明了紧致klt Kähler簇的每个满射自同态都能提升到合适的极大拟平展覆盖上。
英文摘要
We study compact Kähler varieties admitting int-amplified endomorphisms from the viewpoint of positivity of tangent sheaves. Our main result shows that the tangent sheaf of such a variety is weakly positively curved; in particular, it is pseudo-effective in a strong sense. This establishes a new link between complex dynamics and the positivity theory of tangent sheaves, and provides an alternative to equivariant MMP techniques in the compact Kähler setting. As an application, we prove a Kähler analogue of Yoshikawa's structure theorem: for a compact Kähler klt variety admitting an int-amplified endomorphism, after an equivariant quasi-étale cover, it admits an equivariant flat MRC fibration with irreducible fibres onto a complex torus; in the smooth case, the fibration is smooth whose periodic fibres are of Fano type. To this end, we prove the existence of minimal models in the case of numerical dimension zero canonical divisors for non-projective Kähler varieties. We further study rationally connected manifolds with pseudo-effective tangent bundle, focusing on their relation to Fano-type properties, almost homogeneity, and fundamental groups. In the proof, we also show that every surjective endomorphism of a compact klt Kähler variety lifts to a suitable maximally quasi-étale cover.
Comments38 pages, comments are welcome
