Extensions in MHM and Hain's Biextension Line Bundle - Part 2

Delve into the intricacies of biextension line bundles and their extensions in this 58-minute lecture by Patrick Brosnan from the University of Maryland. Explore the analytic line bundle L, associated with pairs of normal functions on a complex manifold U. Learn about Brosnan and Pearlstein's findings regarding the extension of L to a line bundle on a projective variety S, and its canonical extension as a Q-line bundle. Examine the topological invariant of normal functions represented by the first Chern class of L in the cohomology of U. Gain insights into the historical context of these computations, tracing back to foundational papers by Hain and Hain-Reed. Conclude with a formula for the Q-line bundle, providing a deeper understanding of these complex mathematical concepts.