Torsion in Griffiths Groups

TL;DR

This paper demonstrates the existence of smooth complex projective varieties with infinitely many torsion elements of arbitrary order in their third Griffiths group, extending previous results for order 2.

Contribution

It generalizes Schreieder's theorem by constructing varieties with torsion elements of any order in their Griffiths groups.

Findings

Existence of varieties with infinite torsion in Griffiths groups for any order n

Extension of Schreieder's result from n=2 to all n≥2

Construction of specific 5-dimensional varieties with these properties

Abstract

We show that for any integer $n\geq2$ there is a smooth complex projective variety $X$ of dimension $5$ whose third Griffiths group $\text{Griff}^{3}(X)$ contains infinitely many torsion elements of order $n$. This generalises a recent theorem of Schreieder who proved the result for $n=2$.