Degenerations of Hodge structure
arXiv:1607.00933
Abstract
Two interesting questions in algebraic geometry are: (i) how can a smooth projective varieties degenerate? and (ii) given two such degenerations, when can we say that one is "more singular/degenerate" than the other? Schmid's Nilpotent Orbit Theorem yields Hodge-theoretic analogs of these questions, and the Hodge-theoretic answers in turn provide insight into the motivating algebro-geometric questions, sometimes with applications to the study of moduli. Recently the Hodge-theoretic questions have been completely answered. This is an expository survey of that work.
Expository notes for the Algebraic Geometry Summer Research Institute Graduate Student Bootcamp in Salt Lake City, Utah, July 06--10, 2015