论文标题
大的PICARD定理和代数的4sbolicities属于霍奇结构的变化
Big Picard theorems and algebraic hyperbolicity for varieties admitting a variation of Hodge structures
论文作者
论文摘要
在本文中，我们研究了准混合的Kähler歧管$ u $的各种双曲线性能，该特性接受了Hodge结构的复杂极化变化，因此周期图的每个光纤都是零维的。在第一部分中，我们证明$ u $是代数双曲线，并且广义的Big Picard定理以$ u $为单位。在第二部分中，我们证明有有限的o $ \ tilde {u} $ $ u $从quasi-projective歧管$ \ tilde $ \ tilde {u} $中，以便任何投射的projective compactification $ x $ x $ of $ x $ of $ \ tilde {u} $ is picard tilde {u tilde {u tilde {u $ x $ of $ x- \ tilde {u} $中没有包含的$ x $。该结果粗略地融合了Nadel，Rousseau，Brunebarbe和Cadorel的先前作品，涉及通过无扭转的晶格的界面对称域商的压缩物的高光质。
In this paper, we study various hyperbolicity properties for a quasi-compact Kähler manifold $U$ which admits a complex polarized variation of Hodge structures so that each fiber of the period map is zero-dimensional. In the first part, we prove that $U$ is algebraically hyperbolic and that the generalized big Picard theorem holds for $U$. In the second part, we prove that there is a finite étale cover $\tilde{U}$ of $U$ from a quasi-projective manifold $\tilde{U}$ such that any projective compactification $X$ of $\tilde{U}$ is Picard hyperbolic modulo the boundary $X-\tilde{U}$, and any irreducible subvariety of $X$ not contained in $X-\tilde{U}$ is of general type. This result coarsely incorporates previous works by Nadel, Rousseau, Brunebarbe and Cadorel on the hyperbolicity of compactifications of quotients of bounded symmetric domains by torsion-free lattices.
