The zero locus of an admissible normal function

TL;DR

This paper proves that the zero locus of an admissible normal function over an algebraic curve is algebraic, establishing a significant connection between complex analysis and algebraic geometry.

Contribution

It demonstrates the algebraicity of the zero locus for admissible normal functions specifically over algebraic curves.

Findings

Zero locus of admissible normal functions over curves is algebraic.

Provides a proof connecting normal functions and algebraic geometry.

Enhances understanding of the structure of normal functions in algebraic settings.

Abstract

We prove that the zero locus of an admissible normal function over an algebraic parameter space S is algebraic in the case where S is a curve.