论文标题
几乎是准阴性的全态截面曲率
On almost quasi-negative holomorphic sectional curvature
论文作者
论文摘要
最近著名的diverio-trapani定理和吴云的定理指出，紧凑的kähler歧管承认，准单调的荷兰截面曲率的kähler指标具有宽敞的规范线束，确认了Yau的猜想。在本文中，我们将考虑一个几乎准阴性的圆形截面曲率的自然概念，并将该定理扩展到紧凑的kähler歧管几乎是准阴性的全态截面曲率的歧管。我们还获得了不平等$ \ int_xc_1（k_x）^n> 0 $的gap-type定理。在讨论中，我们引入了一个圆形截面曲率负面部分的能力概念，该曲率在研究几乎准确的全体形态截面曲率和规范线束的扩张之间起着关键作用。
A recent celebrated theorem of Diverio-Trapani and Wu-Yau states that a compact Kähler manifold admitting a Kähler metric of quasi-negative holomorphic sectional curvature has an ample canonical line bundle, confirming a conjecture of Yau. In this paper we shall consider a natural notion of almost quasi-negative holomorphic sectional curvature and extend this theorem to compact Kähler manifolds of almost quasi-negative holomorphic sectional curvature. We also obtain a gap-type theorem for the inequality $\int_Xc_1(K_X)^n>0$ in terms of the holomorphic sectional curvature. In the discussions, we introduce a capacity notion for the negative part of holomorphic sectional curvature, which plays a key role in studying the relation between the almost quasi-negative holomorphic sectional curvature and ampleness of the canonical line bundle.
