Journal of Algebraic Geometry

Journal of Algebraic Geometry

Online ISSN 1534-7486; Print ISSN 1056-3911

   
 
 

 

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


Author: Elisabetta Colombo
Journal: J. Algebraic Geom. 11 (2002), 761-790
DOI: https://doi.org/10.1090/S1056-3911-02-00332-6
Published electronically: June 10, 2002
MathSciNet review: 1910986
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Abstract | References | Additional Information

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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Additional Information

Elisabetta Colombo
Affiliation: Dipartimento di Matematica, Universita’ di Milano, via Saldini 50, 20133 Milano, Italy
Email: elisabetta.colombo@mat.unimi.it

DOI: https://doi.org/10.1090/S1056-3911-02-00332-6
Received by editor(s): August 1, 2000
Published electronically: June 10, 2002
Additional Notes: The author acknowledges support from MURST and GNSAGA (CNR) Italy

American Mathematical Society