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

Elisabetta Colombo

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arXiv · math/0201244

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

Elisabetta Colombo

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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.

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Elisabetta Colombo. 2002-01-25. The mixed Hodge structure on the fundamental group of hyperelliptic curves and higher cycles. https://arxiv.org/abs/math/0201244

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