The Projectivity of Compact Kähler Manifolds with Mixed Curvature Condition

Litao Han, Chang Li, Yangxiang Lu
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Abstract

In a recent paper, Li–Ni–Zhu study the nefness and ampleness of the canonical line bundle of a compact Kähler manifold with \(\textrm{Ric}_k\leqslant 0\) and provide a direct alternate proof to a recent result of Chu–Lee–Tam. In this paper, we generalize the method of Li–Ni–Zhu to a more general setting which concerning the connection between the mixed curvature condition and the positivity of the canonical bundle. The key point is to do some a priori estimates to the solution of a Mong-Ampère type equation.

Abstract Image

具有混合曲率条件的紧凑凯勒流形的投影性
在最近的一篇论文中,李-尼-朱研究了具有\(\textrm{Ric}_k\leqslant 0\) 的紧凑凯勒流形的典型线束的无穷性和振幅性,并对朱-李-谭(Chu-Lee-Tam)最近的一个结果提供了直接的替代证明。在本文中,我们将李-尼-朱的方法推广到一个更一般的环境中,其中涉及混合曲率条件与正典束的正向性之间的联系。关键是对蒙-安培方程的解进行一些先验估计。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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