Wanlin Li

Affiliation: Vanderbilt University

Title Of Talk: Algebraic cycles associated to curves

Abstract: Following the work of Griffiths, a homologically trivial algebraic cycle characterizes a class of extensions of mixed Hodge structures. Furthermore, a family of such cycles characterizes a variation of mixed Hodge structures in the form of a normal function. In the work of Hain, quotients of the fundamental group of a curve in its lower central series carry mixed Hodge structures, and there exist normal functions over the moduli of curves associated with them. For curves of genus g>2, there exists a normal function over M_g associated to the Ceresa cycle/modified diagonal cycle corresponding to the Hodge structure on the second nilpotent quotient of the fundamental group. This normal function vanishes on the hyperelliptic loci. In this talk, I will discuss some recent developments on the study of cycles constructed from algebraic curves.

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