A Guide to Variations of Mixed Hodge Structure - Generalities and Examples

Explore a comprehensive lecture on variations of mixed Hodge structure over smooth varieties. Delve into basic facts about admissible variations and learn how to compute the mixed Hodge structure (MHS) on fibers under favorable conditions. Examine the use of global monodromy representation and iterated integrals in this process. Understand the fundamental concept of mixed Hodge structure on the completion of the path torsor relative to the associated weight graded variation. Discover how to determine the MHS on one fiber from another using the completed torsor of paths. Investigate the reconstruction of entire variations from known fibers. Apply these concepts to a practical example involving the elliptic KZB variation of MHS over the universal elliptic curve with its identity section removed.