Geodesic
Big Picard theorems and algebraic hyperbolicity for varieties admitting a variation of Hodge structures
Épijournal de Géométrie Algébrique, Tome 7 (2023)

Voir la notice de l'article provenant de la source Episciences

In this paper, we study various hyperbolicity properties for a quasi-compact K"ahler 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. 
@article{10_46298_epiga_2023_volume7_8393,
     author = {Deng, Ya},
     title = {Big {Picard} theorems and algebraic hyperbolicity for varieties admitting a variation of {Hodge} structures},
     journal = {\'Epijournal de G\'eom\'etrie Alg\'ebrique},
     publisher = {mathdoc},
     volume = {7},
     year = {2023},
     doi = {10.46298/epiga.2023.volume7.8393},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.46298/epiga.2023.volume7.8393/}
}
TY  - JOUR
AU  - Deng, Ya
TI  - Big Picard theorems and algebraic hyperbolicity for varieties admitting a variation of Hodge structures
JO  - Épijournal de Géométrie Algébrique
PY  - 2023
VL  - 7
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/articles/10.46298/epiga.2023.volume7.8393/
DO  - 10.46298/epiga.2023.volume7.8393
LA  - en
ID  - 10_46298_epiga_2023_volume7_8393
ER  - 
%0 Journal Article
%A Deng, Ya
%T Big Picard theorems and algebraic hyperbolicity for varieties admitting a variation of Hodge structures
%J Épijournal de Géométrie Algébrique
%D 2023
%V 7
%I mathdoc
%U http://geodesic.mathdoc.fr/articles/10.46298/epiga.2023.volume7.8393/
%R 10.46298/epiga.2023.volume7.8393
%G en
%F 10_46298_epiga_2023_volume7_8393
Deng, Ya. Big Picard theorems and algebraic hyperbolicity for varieties admitting a variation of Hodge structures. Épijournal de Géométrie Algébrique, Tome 7 (2023). doi: 10.46298/epiga.2023.volume7.8393

Cité par Sources :