Raymond Cheng, Department of Pure Mathematics, University of Waterloo
“Variations on a Theme of Hodge, Variation I: Deformations”
As we have seen, the cohomology of Kahler manifolds posses fine linear algebraic structure coming from the complex and Kahler structures on the underlying topological space. What does this structure say about the geometry and topology of the manifold? Our first glimpse of how Hodge structures give insight to geometry will be through variations of Hodge structures arising from deformations of Kahler manifolds. To set the stage for our eventual discussion of variations, I will discuss the notion of deformations of a complex manifold and introduce the Kodaira-Spencer map. Along with the technical concepts in deformation theory, I hope to discuss why abstract Hodge structures are defined as they are.
MC 5479