Geometric Perspective on Piecewise Polynomiality of Double Hurwitz Numbers. Issue 4 (1st December 2014)

• Record Type: Journal Article
• Authors: Cavalieri, Renzo; Marcus, Steffen
• Is Part Of: Canadian mathematical bulletin =. Volume 57:Issue 4(2014)
• Page Start: 749
• Page End: 764
• Publication Date: 2014-12-01
• Subjects: 14N35; double Hurwitz numbers -- wall crossings -- moduli spaces -- ELSV formula; Mathematics -- Periodicals; Mathematics; Periodicals; 510.5
• DOI: 10.4153/CMB-2014-031-6
• Languages: English
• ISSNs: 0008-4395

Abstract

Abstract: 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).