École polytechnique – Centre de Mathématiques Laurent Schwartz

14h00-15h30 – Ya Deng (IHÉS)

"Big Picard theorem for varieties admitting a variation of Hodge structure"

Abstract: For a quasi-projective variety U which admits a polarized variation of Hodge structures with quasi-finite period map, we prove that any holomorphic map from the punctured disk to U extends to a holomorphic map of the disk into any projective compactification of U. This can be seen as a generalized big Picard theorem. In particular any holomorphic map from a quasi-projective variety to U is algebraic. This extends and strengthens a previous work by Bakker-Brunebarbe-Tsimerman, in which they prove the algebraicity of analytic maps under the extra assumption that monodromy groups of VHS are arithmetic.