שמור ב:
| מחבר ראשי: | |
|---|---|
| פורמט: | Preprint |
| יצא לאור: |
2020
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| נושאים: | |
| גישה מקוונת: | https://arxiv.org/abs/2001.04426 |
| תגים: |
הוספת תג
אין תגיות, היה/י הראשונ/ה לתייג את הרשומה!
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תוכן הענינים:
- 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.