Higher normal functions and Griffiths groups

Abstract

In this paper we present some results on the problem of identifying algebraic cycles by means of periods of integrals. The key idea is to combine the two main streams in the study of algebraic cycles. One is the theory of normal functions and Abel-Jacobi maps originally developed by Griffiths. Another is the Bloch-Beilinson’s (conjectural) filtration on Chow groups arising from the theory of mixed motives. The outcome is the theory of higher normal functions and higher Abel-Jacobi maps, which we apply to the study of algebraic cycles on hypersurfaces in $\mathbb {P}^n$.