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
本文证明具有商奇点且切层伪有效的紧致Kähler流形经有限拟平展覆盖后平坦纤维化为复环面，纤维有理连通，并在klt情形及射影、低维情形下推广。
AI 中文摘要
本文讨论了关于切层在强意义下伪有效的紧致Kähler流形的几何学的最新进展和开放问题。作为我们的主要结果，我们证明了，在通过一个有限拟平展覆盖之后，任何具有商奇点和伪有效切层的紧致Kähler流形都容许一个到复环面上的平坦纤维化，其纤维为有理连通纤维。我们还获得了klt紧致Kähler流形的类似结构定理，假设在数值维数为零的情形下极小模型存在；因此，该结果在射影情形和低维紧致Kähler流形中无条件成立。
英文摘要
In this paper, we discuss recent developments and open problems concerning the geometry of compact Kähler varieties whose tangent sheaves are pseudo-effective in a strong sense. As our main result, we prove that, after passing to a finite quasi-étale cover, any compact Kähler variety with quotient singularities and pseudo-effective tangent sheaf admits a flat fibration onto a complex torus, with rationally connected fibers. We also obtain an analogous structure theorem for klt compact Kähler varieties, assuming the existence of minimal models in numerical dimension zero; consequently, the result holds unconditionally in the projective setting and for low-dimensional compact Kähler varieties.
Comments18 Pages, comments are welcome; submitted for a possible publication in the proceeding of AGEA2025
