## Mixed Hodge Structures of Siegel Modular Varieties and Siegel Eisenstein Series

J. Math. Sci. Univ. Tokyo
Vol. 3 (1996), No. 2, Page 297--330.

Miyazaki, Takuya
Mixed Hodge Structures of Siegel Modular Varieties and Siegel Eisenstein Series
In this paper we study the mixed Hodge structure on the middle degree cohomology of the Siegel modular variety of level $n$. We attach some global automorphic forms to its highest weight quotient space and also show a vanishing of the next weight quotient. As an appendix, we also consider the universal family of abelian varieties over the moduli space and treat its middle degree mixed Hodge structure similar to the above case.