Limits and singularities of normal functions

Research output: Contribution to journalArticlepeer-review

Abstract

We find a new method to detect the linearly independence of R-regulator indecomposable K1-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 P3 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 languageEnglish (US)
Pages (from-to)1401-1437
Number of pages37
JournalEuropean Journal of Mathematics
Volume7
Issue number4
DOIs
StatePublished - Dec 2021

Keywords

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

ASJC Scopus subject areas

  • Mathematics(all)

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