## 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 P3×P1×P1 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.

Original language | English (US) |
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Pages (from-to) | 1401-1437 |

Number of pages | 37 |

Journal | European Journal of Mathematics |

Volume | 7 |

Issue number | 4 |

DOIs | |

State | Published - Dec 2021 |

## Keywords

- Algebraic cycles
- Higher Chow groups
- Higher regulators
- K3 surfaces
- Variation of Hodge structures

## ASJC Scopus subject areas

- Mathematics(all)