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

2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/63200In 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.22 pages, 3 figures. To appear in: Journal of Algebraic GeometryAlgebraic GeometryPrimary 14C30; Secondary 14C25,14H30The mixed Hodge structure on the fundamental group of hyperelliptic curves and higher cyclestext