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On Weierstrass points of a family of quartic curves. (English) Zbl 1334.14020

Summary: The aim of this paper is to investigate properties of the Weierstrass points on the family of compact Riemann surfaces \(C_{a,b,c}:X^4+Y^4+Z^4+aX^2Y^2+bX^2Z^2+cY^2Z^2=0\), where \(a,b\) and \(c\) are parameters such that \(a^2,b^2,c^2\neq 1,4\) and \(a^2+b^2+c^2-abc-4\neq 0\), by using finite group actions on this family. Furthermore, the geometry of these points is discussed.

MSC:

14H55 Riemann surfaces; Weierstrass points; gap sequences
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References:

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