发表机构
Université Côte d’Azur; CNRS, Institut de Mathématiques de Jussieu-Paris Rive Gauche, Sorbonne Université; Tohoku University（蔚蓝海岸大学; 法国国家科学研究中心，朱西厄-巴黎左岸数学研究所，索邦大学; 东北大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文将Höring–Peternell的平坦性准则从射影簇推广至凯勒空间，证明klt紧凯勒空间上第一陈类为零的伪有效层经有限拟平覆盖后自反拉回局部自由且平坦，核心依赖两项新结果。
AI 中文摘要
本文证明：若E是klt紧凯勒空间X上第一陈类为零的伪有效层，则经过有限拟平覆盖后，E的自反拉回是局部自由且平坦的。这将Höring–Peternell最初针对射影簇建立的平坦性准则推广到了凯勒情形。证明依赖于两个核心新结果（即使在射影情形下也是新的）：其一为稳定层的平坦性定理，即斜率稳定且第一陈类为零的伪有效层是埃尔米特平坦的，该结论结合了埃尔米特-爱因斯坦理论与直像层的次调和性质；其二为辛普森平坦性定理的奇异凯勒类比，适用于局部自由埃尔米特平坦层的扩张。
英文摘要
In this paper, we prove that if $E$ is a pseudo-effective sheaf with vanishing first Chern class on a klt compact Kähler space $X$, then, after passing to a finite quasi-étale cover, the reflexive pullback of $E$ is locally free and flat. This extends the flatness criterion of Höring--Peternell, originally established for projective varieties, to the Kähler setting. The proof relies on two main ingredients, both of which are new even in the projective case. The first is a flatness theorem for stable sheaves: we show that a slope-stable pseudo-effective sheaf with vanishing first Chern class is Hermitian flat. This is obtained by combining Hermitian--Einstein theory with the subharmonicity properties of direct image sheaves. The second is a singular Kähler analogue of Simpson's flatness theorem for extensions of locally free Hermitian flat sheaves.
Comments40 pages, comments are welcome
