Degeneration of mixed Hodge structures  

Kazuya Kato

Abstract.

This is a joint work with Chikara Nakayama and Sampei Usui. In his great 
works on degeneration of mixed Hodge structures, Masaki Kashiwara 
formulated the notion "infinitesimal mixed Hogde module (IMHM)". IMHM 
appears when a variation of mixed Hodge structure degenerates.
Nakayama, Usui and I obtained the theory of partial toroidal 
compactifications of the  classifying spaces of mixed Hodge structures 
whose graded quotients are polarized. The points at infinity of these 
enlarged spaces are  the classes of IMHM.