TY - JOUR

T1 - MR 2944715 Reviewed Zhu S. On the recursion formula for double Hurwitz numbers. Proceedings of the American Mathematical Society (2012) 140, no. 11, 3749--3760. (Reviewer Francesca Vetro) 14H30 (05E05 14H10)

AU - Vetro, Francesca

PY - 2013

Y1 - 2013

N2 - Let $\mu = (\mu_{1}, \mu_{2}, \ldots, \mu_{m})$ and $\nu = (\nu_{1}, \nu_{2}, \ldots, \nu_{n})$ be two partitions of a positive integer $d$. In this paper, the author considers degree $d$ branched coverings of $\mathbb{P}^{1}$ with at most two special points, $0$ and $\infty$. Specifically, the purpose of the author is to give a recursion formula for double Hurwitz numbers $H^{g}_{\mu, \nu}$ by the cut-join analysis. Here, $H^{g}_{\mu, \nu}$ denotes the number of genus $g$ branched covers of $\mathbb{P}^{1}$ with branching date corresponding to $\mu$ and $\nu$ over $0$ and $\infty$, respectively. Furthemore, as application, the author gets a polynomial identity for linear Goulden-Jackson-Vakil intersection numbers.

AB - Let $\mu = (\mu_{1}, \mu_{2}, \ldots, \mu_{m})$ and $\nu = (\nu_{1}, \nu_{2}, \ldots, \nu_{n})$ be two partitions of a positive integer $d$. In this paper, the author considers degree $d$ branched coverings of $\mathbb{P}^{1}$ with at most two special points, $0$ and $\infty$. Specifically, the purpose of the author is to give a recursion formula for double Hurwitz numbers $H^{g}_{\mu, \nu}$ by the cut-join analysis. Here, $H^{g}_{\mu, \nu}$ denotes the number of genus $g$ branched covers of $\mathbb{P}^{1}$ with branching date corresponding to $\mu$ and $\nu$ over $0$ and $\infty$, respectively. Furthemore, as application, the author gets a polynomial identity for linear Goulden-Jackson-Vakil intersection numbers.

UR - http://hdl.handle.net/10447/103605

UR - http://www.ams.org

M3 - Review article

VL - 2013

JO - MATHEMATICAL REVIEWS

JF - MATHEMATICAL REVIEWS

SN - 0025-5629

ER -