2022/07/29 by Spencer Bloch, Bloch, Spencer, Robin de Jong +3
Arts and Humanities · Mathematics · #11G50 #14D06 #14D07 #14J20 #14J70 #14Q15 #14Q20 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Historical Studies and Socio-cultural Analysis #Number Theory (math.NT)
paper · pdf · doi:10.48550/arxiv.2208.00017
openalex publication_date 2022/07/29 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We consider the problem of explicitly computing Beilinson--Bloch heights of homologically trivial cycles on varieties defined over number fields. Recent results have established a congruence, up to the rational span of logarithms of primes, between the height of certain limit mixed Hodge structures and certain Beilinson--Bloch heights obtained from odd-dimensional hypersurfaces with a node. This congruence suggests a new method to compute Beilinson--Bloch heights. Here we explain how to compute the relevant limit mixed Hodge structures in practice, then apply our computational method to a nodal quartic curve and a nodal cubic threefold. In both cases, we explain the nature of the primes occurring in the congruence.