Geometric Perspective on Piecewise Polynomiality of Double Hurwitz Numbers

Canadian mathematical bulletin

Renzo Cavalieri²  Steffen Marcus¹ 

[1] Department of Mathematics, University of Utah, E Room 233, Salt Lake City, UT 84112, U.S.A;Colorado State University, Department of Mathematics, Weber Building, Fort Collins, CO 80523, U.S.A

关键词: double Hurwitz numbers;    wall crossings;    moduli spaces;    ELSV formula;   

DOI  :  10.4153/CMB-2014-031-6

学科分类：数学（综合）

来源: University of Toronto Press * Journals Division

【 摘 要 】

We describe double Hurwitz numbers as intersection numbers on themoduli space of curves $overline{mathcal{M}}_{g,n}$. Using a result on thepolynomiality of intersection numbers of psi classes with the DoubleRamification Cycle, our formula explains the polynomiality in chambersof double Hurwitz numbers, and the wall crossing phenomenon in termsof a variation of correction terms to the $psi$ classes. Weinterpret this as suggestive evidence for polynomiality of the DoubleRamification Cycle (which is only known in genera $0$ and $1$).

【 授权许可】

Unknown