Complex-symbolic seminar, November 3

 Matthias Wagner (EPF, Lausanne):
 

On the uniformization of hyperelliptic curves
 

Abstract.
Consider a hyperelliptic algebraic curve   S   of the form
 

  w² = (z-a₁)...(z-a_2g+2)

where the genus   g>1   and the   a_i   in  C  are pairwise distinct. The uniformization theorem of Poincar\'e tells us that there exists a group    Gamma  isomorphic to    pi₁(S)   such that    H/ Gamma   is biholomorphically equivalent to   S, where    H    is the upper halfplane. In this talk we will show a way to do the step from the curve   S   to the group   Gamma   numerically.