论文标题
复杂的Hessian方程的Nakai-Moishezon标准
Nakai-Moishezon criterions for complex Hessian equations
论文作者
论文摘要
唐纳森（Donaldson）提出的$ j $ - 方程是Kähler歧管上的一个复杂的Hessian商。 $ j $ quation的解决性证明，歌曲 - 韦克科夫（Song-Weinkove）等同于订阅的存在。 Lejmi-Szekelyhidi也猜想，就霍明型相交数字而言，这是稳定条件，作为代数几何形状中Nakai-Moishezon标准的类似物。最近，陈在较强的统一稳定性条件下证明了猜想。在本文中，我们为分析Kähler品种成对的Kähler类建立了Nakai-Moishezon型标准。结果，我们证明了Lejmi-Szekelyhidi对$ j $ equation的原始猜想。我们还应用这样的标准以在平滑最小模型上获得恒定标态曲率Kähler指标的家族。
The $J$-equation proposed by Donaldson is a complex Hessian quotient equation on Kähler manifolds. The solvability of the $J$-equation is proved by Song-Weinkove to be equivalent to the existence of a subsolution. It is also conjectured by Lejmi-Szekelyhidi to be equivalent to a stability condition in terms of holomorphic intersection numbers as an analogue of the Nakai-Moishezon criterion in algebraic geometry. The conjecture is recently proved by Chen under a stronger uniform stability condition. In this paper, we establish a Nakai-Moishezon type criterion for pairs of Kähler classes on analytic Kähler varieties. As a consequence, we prove Lejmi-Szekelyhidi's original conjecture for the $J$-equation. We also apply such a criterion to obtain a family of constant scalar curvature Kähler metrics on smooth minimal models.
