On the number of coverings of the sphere ramified over given points
arXiv:1312.1141
Abstract
We present the generating function for the numbers of isomorphism classes of coverings of the two-dimensional sphere by the genus compact oriented surface not ramified outside of a given set of points in the target, fixed ramification type over one point, and arbitrary ramification types over the remaining points. We present the genus expansion of this generating function and prove, that the generating function of coverings of genus satisfies some system of differential equations. We show that this generating function is a specialization of the function from paper \cite{GJ} and, therefore, satisfies the KP-hierarchy.
14 pages