Period maps at infinity

Abstract

Let $\overline{B}$ be a smooth projective varieity, and $Z \subset \overline{B}$ a simple normal crossing divisor. Assume that $B = \overline{B} - Z$ admits a variation of pure, polarized Hodge structure. The divisor $Z$ is naturally stratified, and Schmid's nilpotent orbit theorem defines a family/variation of nilpotent orbits along each strata. We study the rich geometric structure encoded by this family, its relationship to the induced (quotient) variation of pure Hodge structure on the strata, and establish a relationship between the extension data in the nilpotent orbits and the normal bundles of the smooth irreducible components of $Z$.