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arXiv · 1707.02261

Extending the double ramification cycle by resolving the Abel-Jacobi map

David Holmes
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Abstract

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.

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David Holmes. 2017-07-07. Extending the double ramification cycle by resolving the Abel-Jacobi map. https://doi.org/10.1017/s1474748019000252

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