A geometric perspective on the piecewise polynomiality of double Hurwitz numbers
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 classes. We interpret this as suggestive evidence for polynomiality of the Double Ramification Cycle.
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