Can be used for studying algebraic cycles.
Charles: On the zero locus of normal functions and the étale Abel-Jacobi map. http://arxiv.org/abs/0902.1948
arXiv:0910.0628 On the algebraicity of the zero locus of an admissible normal function from arXiv Front: math.AG by Patrick Brosnan, Gregory Pearlstein We show that the zero locus of an admissible normal function on a smooth complex algebraic variety is algebraic.
nLab page on Normal functions