Abstract
We find a new method to detect the linearly independence of R-regulator indecomposable K-1-cycles which is based on the singularities and limits of admissible normal functions. We also construct a collection of higher Chow cycles on certain surfaces in P-3 of degree d >= 4 which degenerate to an arrangement of d planes in general position. By applying our method, we show that these higher Chow cycles are enough to show the surjectivity of the real regulator map when d = 4. Hence our 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 general semistable degeneration family of degree d + 1 threefolds in P-3 xP(1) xP(1) such that a codimension 1 stratum is a surface of the above type. The real regulator indecomposability of our higher Chow cycles implies that the Griffiths group of the general fiber of these threefolds is non-trivial.
