Institut für Mathematik


Modul:   MAT770  Oberseminar: Algebraische Geometrie

Big Picard theorem for varieties admitting variations of Hodge structures

Vortrag von Dr. Ya Deng

Datum: 16.03.20  Zeit: 13.15 - 14.45  Raum: Y27H25 CANCELLED

For a quasi-projective variety \(U\) which admits a polarised variation of Hodge structures (PVHS) 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 generalised big Picard theorem. In particular any holomorphic map from a quasi-projective variety to U is algebraic. This extends a previous work by Bakker-Brunebarbe-Tsimerman, in which they prove the algebraicity of analytic maps under the additional assumption that monodromy groups of PVHS are arithmetic. If time permits, I will present another related work (jointly with Lu-Sun-Zuo) on the big Picard theorem for moduli spaces of polarised manifolds.