Real Regulators on Self-Products of K3 Surfaces

TL;DR

This paper introduces a new regulator class on the self-product of K3 surfaces using an archimedean pairing, linking geometry, deformation theory, and higher Chow groups.

Contribution

It constructs a regulator indecomposable K_1-class on a self-product of a K3 surface using a novel archimedean pairing, connecting it to Bloch's higher Chow groups.

Findings

Constructed a regulator indecomposable K_1-class

Linked the pairing to Bloch's higher Chow groups

Applied to geometry and deformation theory of K3 surfaces

Abstract

Based on a novel application of an archimedean type pairing to the geometry and deformation theory of $K3$ surfaces, we construct a regulator indecomposable $K_1$-class on a self-product of a $K3$ surface. In the Appendix, we explain how this pairing is a special instance of a general pairing on precycles in the equivalence relation defining Bloch's higher Chow groups.