Geometric Perspective on Piecewise Polynomiality of Double Hurwitz Numbers

被引：4

作者：

Cavalieri, Renzo ^{[1
]}

Marcus, Steffen ^{[2
]}

机构：

[1] Colorado State Univ, Dept Math, Ft Collins, CO 80523 USA

[2] Univ Utah, Dept Math, Salt Lake City, UT 84112 USA

来源：

CANADIAN MATHEMATICAL BULLETIN-BULLETIN CANADIEN DE MATHEMATIQUES | 2014年 / 57卷 / 04期

基金：

美国国家科学基金会;

关键词：

double Hurwitz numbers; wall crossings; moduli spaces; ELSV formula; MODULI SPACES; VIRTUAL LOCALIZATION; TAUTOLOGICAL CLASSES; WALL CROSSINGS; CURVES; CYCLES;

D O I：

10.4153/CMB-2014-031-6

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We describe double Hurwitz numbers as intersection numbers on the moduli space of curves 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 psi classes. We interpret this as suggestive evidence for polynomiality of the Double Ramification Cycle (which is only known in genera 0 and 1).

引用

页码：749 / 764

页数：16

共 17 条

[1]

[Anonymous], ARXIV12063534

[2]

[Anonymous], ARXIV12115273

[3]

[Anonymous], ARXIV12067001

[4] Polynomiality, wall crossings and tropical geometry of rational double Hurwitz cycles [J].

Bertram, Aaron ;

Cavalieri, Renzo ;

Markwig, Hannah .

JOURNAL OF COMBINATORIAL THEORY SERIES A, 2013, 120 (07) :1604-1631

[5] Wall crossings for double Hurwitz numbers [J].

Cavalieri, Renzo ;

Johnson, Paul ;

Markwig, Hannah .

ADVANCES IN MATHEMATICS, 2011, 228 (04) :1894-1937

[6] Hurwitz numbers and intersections on moduli spaces of curves [J].

Ekedahl, T ;

Lando, S ;

Shapiro, M ;

Vainshtein, A .

INVENTIONES MATHEMATICAE, 2001, 146 (02) :297-327

[7]

Eliashberg Y, 2000, GEOM FUNCT ANAL, P560

[8]

Faber C, 2005, J EUR MATH SOC, V7, P13

[9] Towards the geometry of double Hurwitz numbers [J].

Goulden, IP ;

Jackson, DM ;

Vakil, R .

ADVANCES IN MATHEMATICS, 2005, 198 (01) :43-92

[10] Relative virtual localization and vanishing of tautological classes on moduli spaces of curves [J].

Graber, T ;

Vakil, R .

DUKE MATHEMATICAL JOURNAL, 2005, 130 (01) :1-37

← 1 2 →