Singularities of admissible normal functions
Speaker: Zhaohu Nie, PSU-Altoona
Abstract: The first proof of the Lefschetz (1,1) theorem was given by Poincare and Lefschetz using normal functions for a Lefschetz pencil. The hope to generalize this method to higher codimensional Hodge conjecture was blocked by the failure of Jacobian inversion. In another direction, one can hope for an inductive proof of the Hodge conjecture if for any primitive Hodge class one can find a, necessarily singular, hypersurface to "capture part of it". Recently Green and Griffiths introduced the notion of extended normal functions over higher dimensional bases such that their singular loci corresponds to such hypersurfaces. In this talk, we will present how to understand singularities using the viewpoint of admissible normal functions, and how the Hodge conjecture is then equivalent to the existence of singularities. This is joint work with P. Brosnan, H. Fang and G. Pearlstein.
Room Reservation Information
Room Number: 106 McAllister
Time: 2:30pm - 3:30pm