Non-trivial elements in the Abel-Jacobi kernels of higher dimensional varieties

TL;DR

This paper constructs non-trivial elements in the Abel-Jacobi kernels of higher-dimensional varieties by specializing correspondences with non-trivial Hodge invariants at points with varying transcendence degrees.

Contribution

It introduces a method to produce non-trivial Abel-Jacobi kernel elements in any codimension using specialization of correspondences with Hodge-theoretic invariants.

Findings

Successfully constructs non-trivial elements in Abel-Jacobi kernels

Demonstrates the use of specialization at points with different transcendence degrees

Advances understanding of the structure of Abel-Jacobi kernels in higher dimensions

Abstract

The purpose of this paper is to construct non-trivial elements in the Abel-Jacobi kernels in any codimension by specializing correspondences with non-trivial Hodge-theoretical invariants at points with different transcendence degrees over a subfield in $\CC$.