On the algebraicity of the zero locus of an admissible normal function

TL;DR

This paper proves that the zero locus of an admissible normal function on a smooth complex algebraic variety is an algebraic subset, establishing a significant link between complex analysis and algebraic geometry.

Contribution

It establishes the algebraicity of the zero locus of admissible normal functions, a previously conjectural property in Hodge theory.

Findings

Zero locus is algebraic

Supports conjectures in Hodge theory

Bridges complex analysis and algebraic geometry

Abstract

We show that the zero locus of an admissible normal function on a smooth complex algebraic variety is algebraic.