Zero loci of admissible normal functions with torsion singularities

Abstract

We show that the zero locus of a normal function on a smooth complex algebraic variety $S$ is algebraic provided that the normal function extends to an admissible normal function on a smooth compactification such that the divisor at infinity is also smooth. This result, which has also been obtained recently by M. Saito using a different method [22], generalizes a previous result proved by the authors for admissible normal functions on curves [4]