The geometry of the Deligne-Hodge decomposition

Gregory James Pearlstein, University of Massachusetts Amherst

Abstract

In this thesis we explore variations of mixed Hodge structures, both locally and asymptotically. First, making use of certain distinguished gradings of the Hodge and weight filtrations, I compute the curvature of appropriate classifying spaces and Hodge bundles relative to a natural "mixed" Hodge metric. Second, I obtain appropriate generalizations of the Nilpotent Orbit Theorem for admissible variations, norm estimates, a version of the invariant cycle Theorem, and extend an equivalence of categories theorem of Deligne. Third, I demonstrate the existence of canonical Higgs fields associated to such variations and discuss their relations with a partial interpretation of Mirror Symmetry due to Deligne.

Recommended Citation

Gregory James Pearlstein, "The geometry of the Deligne-Hodge decomposition" (January 1, 1999). Electronic Doctoral Dissertations for UMass Amherst. Paper AAI9932337.
http://scholarworks.umass.edu/dissertations/AAI9932337