Constructing Indecomposable Motivic Cohomology Classes on Algebraic Surfaces

TL;DR

This paper introduces a transcendental method to construct indecomposable motivic cohomology classes in higher Chow groups on algebraic surfaces, providing new examples on K3-surfaces and surfaces of general type.

Contribution

It presents a novel approach to constructing indecomposable classes in motivic cohomology using transcendental techniques, expanding the toolkit for algebraic surface studies.

Findings

Constructed indecomposable classes on K3-surfaces.

Extended methods to surfaces of general type.

Provided explicit examples of motivic cohomology classes.

Abstract

We describe a method to construct indecomposable classes in Bloch's higher Chow group $CH^2(X,1)$ on algebraic surfaces over the complex numbers via transcendental methods and apply it to obtain examples on K3-surfaces and some surfaces of general type.