On Weierstrass Points of a Family of Quartic Curves

The aim of this paper is to investigate properties of the Weierstrass points on the family of compact Riemann surfaces Ca,b,c : X4 + Y4 + Z4 + aX2Y2 + bX2Z2 + cY2Z2 = 0, where a,b and c are parameters such that a2,b2,c2≠1, 4 and a2 + b2 + c2 − abc − 4≠0, by using finite group actions on this family. Furthermore, the geometry of these points is discussed.