Abstract:

In 1972, A. Borel proved generalized big Picard theorem for any hermitian locally symmetric variety : any holomorphic map from the punctured disk to extends to a holomorphic map of the disk into any projective compactification of . In particular any analytic map from a quasi-projective variety to is algebraic. Period domains, introduced by Griffiths in 1969, are classifying spaces for Hodge structures. They are transcendental generalizations of hermitian locally symmetric varieties. In this talk, I will present a generalized big Picard theorem for period domains, which extends the recent work by Bakker-Brunebarbe-Tsimerman.