The mixed Hodge structure on the fundamental group of hyperelliptic curves and higher cycles

2002/01/25 by Elisabetta Colombo, Colombo, Elisabetta
Computer Science · Mathematics · #14H30 #Advanced Algebra and Geometry #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Cryptography and Residue Arithmetic #FOS: Mathematics #Primary 14C30 #Secondary 14C25 #math.AG #msc:14C25 #msc:14C30 #msc:14H30

paper · pdf · doi:10.48550/arxiv.math/0201244

22 pages, 3 figures. To appear in: Journal of Algebraic Geometry

arxiv created 2002/01/25 · openalex publication_date 2002/01/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper we give a geometrical interpretation of an extension of mixed Hodge structures (MHS) obtained from the canonical MHS on the group ring of the fundamental group of a hyperelliptic curve modulo the fourth power of its augmentation ideal. We show that the class of this extension coincides with the regulator image of a canonical higher cycle in a hyperelliptic jacobian. This higher cycle was introduced and studied by Collino.

Citations

• Mapping Class Groups and Moduli Spaces of Curves

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