Geometric Perspective on Piecewise Polynomiality of Double Hurwitz Numbers. Issue 4 (1st December 2014) - Cavalieri, Renzo; Marcus, Steffen
Abstract: We describe double Hurwitz numbers as intersection numbers on the moduli space of curves M_g, n Using a result on the polynomiality of intersection numbers of psi classes with the Double Ramification Cycle, 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 φ classes. We interpret this as suggestive evidence for polynomiality of the Double Ramification Cycle (which is only known in genera 0 and 1).