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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

On the recursion formula for double Hurwitz numbers


Author: Shengmao Zhu
Journal: Proc. Amer. Math. Soc. 140 (2012), 3749-3760
MSC (2010): Primary 14H10; Secondary 05E05
Published electronically: March 12, 2012
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Abstract: In this paper, we will give a recursion formula for double Hurwitz numbers by the cut-join analysis. This recursion formula can be considered as a generalized version of the recursion formula for simple Hurwitz numbers derived by Mulase and Zhang. As a direct application, we get a polynomial identity for Goulden-Jackson-Vakil's conjectural intersection numbers and an explicit recursion formula for the computation of these intersection numbers with only $ \psi $-classes.


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Additional Information

Shengmao Zhu
Affiliation: Department of Mathematics and Center of Mathematical Sciences, Zhejiang University, Hangzhou, Zhejiang 310027, People’s Republic of China
Email: zhushengmao@gmail.com

DOI: http://dx.doi.org/10.1090/S0002-9939-2012-11235-3
PII: S 0002-9939(2012)11235-3
Keywords: Hurwitz numbers, moduli space, cut-join, recursion
Received by editor(s): November 30, 2010
Received by editor(s) in revised form: April 28, 2011
Published electronically: March 12, 2012
Communicated by: Lev Borisov
Article copyright: © Copyright 2012 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.