Moduli space of a family of Riemann surfaces of genus one
by
R. Horiuchi
Faculty of Engineering, Doshisha University, Tatara, Kyotanabe, 610-0321 Japan

We consider a family of Riemann surfaces of genus one, any member of which is represented by three-sheeted coverings of the Riemann sphere with one or two (not three) totally branched points. The family contains all the (equivalence classes of) Riemann surfaces of genus one with one exception (coverings with three totally branched points). The moduli space is obtained as a nine-sheeted covering of the Riemann sphere with a point removed, and can be endowed with complex structure of compact Riemann surface of genus zero with five points removed.

References
[1] R. Horiuchi and M. Shiba, Deformation of a torus by attaching the Riemann sphere, Jour. Reine Angew. Math. 456 (1994), 135-149.
[2] A. Hurwitz, Über Riemann'sche Flächen mit gegebenen Verzweigungspunkten, Math. Ann. 39 (1891), 1-61.

Date received: May 16, 2001

Copyright © 2001 by the author(s). The author(s) of this document and the organizers of the conference have granted their consent to include this abstract in Atlas Conferences Inc. Document # cahk-57.