Geometry Seminar

Date: September 27, 2019

Time: 4:00PM - 5:00PM

Location: BLOC 628

Speaker: Souvik Goswami, Texas A&M University

Title: Height pairing on Bloch's higher cycles and mixed Hodge structures.

Abstract: In a previous work with José Ignacio Burgos, we have studied the higher arithmetic Chow groups. As a by product, an Archimedean height pairing between higher cycles has been defined. Classically, Hain has shown that the Archimedean component of the height pairing between ordinary cycles can be interpreted as the class of a biextension in the category of mixed Hodge structures. In the current work we study the mixed Hodge structure defined by a pair of higher cycles intersecting properly and show that, in a special case, the Archimedean height pairing is one of the periods attached to such mixed Hodge structure. This is joint work in progress with Greg Pearlstein and José Ignacio Burgos.