A proof of a conjecture for the number of ramified coverings of the sphere by the torus

Details A proof of a conjecture for the number of ramified coverings of the sphere by the torus A proof of a conjecture for the number of ramified coverings of the sphere by the torus

1999-02-01

arxiv.org/abs/math/9902009v1

Mathematics

Algebraic Geometry

10 pages

Scientific paper

An explicit expression is obtained for the generating series for the number
of ramified coverings of the sphere by the torus, with elementary branch points
and prescribed ramification type over infinity. This proves a conjecture of
Goulden, Jackson and Vainshtein for the explicit number of such coverings.

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