Geodesic
Geometric Perspective on Piecewise Polynomiality of Double Hurwitz Numbers
Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 749-764

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DOI

We describe double Hurwitz numbers as intersection numbers on the moduli space of curves ${{\overline{M}}_{g,n}}$ 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 $\varphi$ classes. We interpret this as suggestive evidence for polynomiality of the Double Ramification Cycle (which is only known in genera 0 and 1).
DOI : 10.4153/CMB-2014-031-6
Mots-clés : 14N35, double Hurwitz numbers, wall crossings, moduli spaces, ELSV formula 
Cavalieri, Renzo; Marcus, Steffen. Geometric Perspective on Piecewise Polynomiality of Double Hurwitz Numbers. Canadian mathematical bulletin, Tome 57 (2014) no. 4, pp. 749-764. doi: 10.4153/CMB-2014-031-6
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     title = {Geometric {Perspective} on {Piecewise} {Polynomiality} of {Double} {Hurwitz} {Numbers}},
     journal = {Canadian mathematical bulletin},
     pages = {749--764},
     year = {2014},
     volume = {57},
     number = {4},
     doi = {10.4153/CMB-2014-031-6},
     url = {http://geodesic.mathdoc.fr/articles/10.4153/CMB-2014-031-6/}
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