论文标题
Arakelov-Nevanlinna的不平等现象，用于霍奇结构和应用的变化
Arakelov-Nevanlinna inequalities for variations of Hodge structures and applications
论文作者
论文摘要
我们证明，对于任何日志平滑的投影对$（x，d）$，我们证明了第二个主定理类型不等式，因此$ x \ setminus d $支持霍奇结构的复杂两极化变化。这可以看作是Arakelov不平等的Nevanlinna理论类似物，因为由于Deligne，Peters和Jost-Zuo而导致的霍奇结构变化。作为一种应用，我们在这种情况下获得了一种夸张的标准，我们用来得出纳德尔众所周知的双曲性结果的广泛概括。我们证明的第一种成分是对于任何日志平滑的投影对$（x，d）$的第二个主定理类型不等式，因此$ x \ setminus d $ d $支持一个公制，其全体形态截面曲率以负常数为界。我们证明的第二个成分是根据hodge结构变体构建的griffiths-schmid公制的全态截面曲率的明确结合。作为我们方法的副产品，我们还建立了对Pairs $（x，d）$的第二个主要定理类型不等式，以便将$ x \ setminus d $夸张地嵌入$ x $中。
We prove a Second Main Theorem type inequality for any log-smooth projective pair $(X,D)$ such that $X\setminus D$ supports a complex polarized variation of Hodge structures. This can be viewed as a Nevanlinna theoretic analogue of the Arakelov inequalities for variations of Hodge structures due to Deligne, Peters and Jost-Zuo. As an application, we obtain in this context a criterion of hyperbolicity that we use to derive a vast generalization of a well-known hyperbolicity result of Nadel. The first ingredient of our proof is a Second Main Theorem type inequality for any log-smooth projective pair $(X,D)$ such that $X\setminus D$ supports a metric whose holomorphic sectional curvature is bounded from above by a negative constant. The second ingredient of our proof is an explicit bound on the holomorphic sectional curvature of the Griffiths-Schmid metric constructed from a variation of Hodge structures. As a byproduct of our approach, we also establish a Second Main Theorem type inequality for pairs $(X,D)$ such that $X\setminus D$ is hyperbolically embedded in $X$.
