2020/07/12 by José Ignacio Burgos Gil, S. Goswami, Gil, J. I. Burgos +3
Mathematics · #Advanced Algebra and Geometry #Advanced Mathematical Identities #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics
paper · pdf · doi:10.48550/arxiv.2007.06036
openalex publication_date 2020/07/12 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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.