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EXTENDING THE DOUBLE RAMIFICATION CYCLE BY RESOLVING THE ABEL-JACOBI MAP

Part of: Curves

Published online by Cambridge University Press:  20 May 2019

David Holmes Open the ORCID record for David Holmes [Opens in a new window]
David Holmes*
Affiliation:
Universiteit Leiden Mathematisch Instituut, Mathematics, Leiden, 2300 RA, The Netherlands
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Abstract

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Over the moduli space of smooth curves, the double ramification cycle can be defined by pulling back the unit section of the universal jacobian along the Abel–Jacobi map. This breaks down over the boundary since the Abel–Jacobi map fails to extend. We construct a ‘universal’ resolution of the Abel–Jacobi map, and thereby extend the double ramification cycle to the whole of the moduli of stable curves. In the non-twisted case, we show that our extension coincides with the cycle constructed by Li, Graber, Vakil via a virtual fundamental class on a space of rubber maps.

Keywords

curvesjacobianscycles

MSC classification

Primary: 14H10: Families, moduli (algebraic) 14H40: Jacobians, Prym varieties
Type
Research Article
Information
Journal of the Institute of Mathematics of Jussieu , Volume 20 , Issue 1 , January 2021 , pp. 331 - 359
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© Cambridge University Press 2019

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