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The Number of Ramified Coverings of the Sphere by the Double Torus, and a General Form for Higher Genera

✍ Scribed by I.P. Goulden; D.M. Jackson

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
171 KB
Volume
88
Category
Article
ISSN
0097-3165

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✦ Synopsis

An explicit expression is obtained for the generating series for the number of ramified coverings of the sphere by the double torus, with elementary branch points and prescribed ramification type over infinity. Thus we are able to determine various linear recurrence equations for the numbers of these coverings with no ramification over infinity; one of these recurrence equations has previously been conjectured by Graber and Pandharipande. The general form of this series is conjectured for the number of these coverings by a surface of arbitrary genus that is at least two.

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