Generalized Lame equations with finite monodromy


You-Cheng Chou

09:30:00 - 11:00:00

103 , Mathematics Research Center Building (ori. New Math. Bldg.)

NTU-Math/TIMS Undergraduate Thesis Presentation

(台大數學系/台大數學科學中心 學士論文發表)

We study the algebraic form of the symmetric generalized Lame equations which have finite projective monodromy group. In particular, we consider the equation with 3 regular singular points on a flat torus T. We give a complete list of all the group types that occur as the projective monodromy group and give the corresponding parameters in its algebraic form. For the equations with only 1 or 2 regular singular points, we further determine its monodromy group types. The main tool used is the Grothendieck correspondence which gives a bijection between Belyi pairs and dessin d'enfants. By Klein's theorem, we may regard the generalized Lame equation as the pullback of the hypergeometric equations by a Beyli function. Under this setup, our main results consist of a systematic construction on the required dessin.