Limits and Singularities of Normal Functions

TL;DR

This paper constructs higher Chow cycles on surfaces degenerating to plane arrangements, providing a new proof of the Hodge-D-Conjecture for specific K3 surfaces and constructing threefolds with non-trivial Griffiths groups.

Contribution

It introduces a novel construction of higher Chow cycles on degenerating surfaces, offering an explicit proof of the Hodge-D-Conjecture for certain K3 surfaces and producing threefolds with interesting Griffiths groups.

Findings

New explicit proof of the Hodge-D-Conjecture for specific K3 surfaces.

Construction of threefolds with non-trivial Griffiths groups.

Development of higher Chow cycles on degenerating surfaces.

Abstract

We construct a collection of higher Chow cycles on certain surfaces which degenerate to an arrangement of planes in general position. When its degree is 4, this construction gives a new explicit proof of the Hodge-D-Conjecture for a certain type of K3 surfaces. As an application, we also construct a certain type of threefolds with non trivial Griffiths group.