On a variety of Weierstrass data for branched minimal surfaces in Euclidean space

Katsuhiro Moriya

E-mail: katsum@comp.metro-u.ac.jp

Abstract. A moduli space of Weierstrass data for a certain class of algebraic minimal surfaces in $\mathbb{R}^3$ or translation spaces becomes a real analytic variety. In this paper, the defining equations of the variety is obtained in the case the surface is of genus $0$ with two puncture points which coincide with two ramification points of the Gauss map and whose order are equal each other. The moduli space becomes a real algebraic variety.

AMSclassification. Primary 53A10; Secondary 53C42

Keywords. Minimal surface, moduli space