Height Pairing on Higher Cycles and Mixed Hodge Structures
Abstract
For a smooth, projective complex variety, we introduce several mixed Hodge structures associated to higher algebraic cycles. Most notably, we introduce a mixed Hodge structure for a pair of higher cycles which are in the refined normalized complex and intersect properly. In a special case, this mixed Hodge structure is an oriented biextension, and its height agrees with the higher archimedean height pairing introduced in a previous paper by the first two authors. We also compute a non-trivial example of this height given by Bloch-Wigner dilogarithm function. Finally we study the variation of mixed Hodge structures of Hodge-Tate type, and show that the height extends continuously to degenerate situations.
Cite
@article{arxiv.2007.06036,
title = {Height Pairing on Higher Cycles and Mixed Hodge Structures},
author = {J. I. Burgos Gil and S. Goswami and G. Pearlstein},
journal= {arXiv preprint arXiv:2007.06036},
year = {2022}
}
Comments
A few typos were corrected to increase data accuracy. To appear in the Proceedings of the London Math Society