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arXiv · 1310.4040

A geometric perspective on the piecewise polynomiality of double Hurwitz numbers

Renzo Cavalieri·Steffen Marcus
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Abstract

We describe double Hurwitz numbers as intersection numbers on the moduli space of curves. Assuming polynomiality of the Double Ramification Cycle (which is known in genera 0 and 1), our formula explains the polynomiality in chambers of double Hurwitz numbers, and the wall crossing phenomenon in terms of a variation of correction terms to the {\psi} classes. We interpret this as suggestive evidence for polynomiality of the Double Ramification Cycle.

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Renzo Cavalieri, Steffen Marcus. 2013-10-15. A geometric perspective on the piecewise polynomiality of double Hurwitz numbers. https://arxiv.org/abs/1310.4040

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