English

Virasoro constraints and topological recursion for Grothendieck's dessin counting

Combinatorics 2015-12-15 v3

Abstract

We compute the number of coverings of CP1{0,1,}{\mathbb{C}}P^1\setminus\{0, 1, \infty\} with a given monodromy type over \infty and given numbers of preimages of 0 and 1. We show that the generating function for these numbers enjoys several remarkable integrability properties: it obeys the Virasoro constraints, an evolution equation, the KP (Kadomtsev-Petviashvili) hierarchy and satisfies a topological recursion in the sense of Eynard-Orantin.

Keywords

Cite

@article{arxiv.1406.5976,
  title  = {Virasoro constraints and topological recursion for Grothendieck's dessin counting},
  author = {Maxim Kazarian and Peter Zograf},
  journal= {arXiv preprint arXiv:1406.5976},
  year   = {2015}
}

Comments

22 pages, 4 figures; extended version