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.
The mixed Hodge structure on the fundamental group of hyperelliptic curves and higher cycles / E. Colombo. - In: JOURNAL OF ALGEBRAIC GEOMETRY. - ISSN 1056-3911. - 11:4(2002), pp. 761-790.
The mixed Hodge structure on the fundamental group of hyperelliptic curves and higher cycles
E. Colombo
2002
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.File in questo prodotto:
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