The zero locus of the infinitesimal invariant

TL;DR

This paper investigates the zero locus of the infinitesimal invariant of a normal function on a complex manifold, proving its constructibility in the Zariski topology under certain conditions.

Contribution

It establishes the constructibility of the zero locus of the infinitesimal invariant for admissible normal functions on quasi-projective complex manifolds.

Findings

Zero locus is well-defined inside the tangent bundle.

Zero locus is constructible in the Zariski topology.

Results apply to admissible normal functions on quasi-projective manifolds.

Abstract

Let {\nu} be a normal function on a complex manifold X. The infinitesimal invariant of {\nu} has a well-defined zero locus inside the tangent bundle TX. When X is quasi-projective, and {\nu} is admissible, we show that this zero locus is constructible in the Zariski topology.