Zero loci of admissible normal functions with torsion singularities

TL;DR

This paper proves that the zero locus of certain normal functions is algebraic when extended to a compactification with torsion singularities, generalizing previous results and confirming recent independent findings.

Contribution

It establishes the algebraicity of zero loci of admissible normal functions with torsion singularities on compactified varieties, extending prior work on curves.

Findings

Zero locus is algebraic under specified conditions

Extension to compactification with torsion singularities is key

Generalizes previous results for curves

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 a admissible normal function on a smooth compactification of S with torsion singularity. This result generalizes our previous result for admissible normal functions on curves [arxiv:math/0604345 [math.AG]]. It has also been obtained by M. Saito using a different method in a recent preprint [arXiv:0803.2771v2].