Classification of 1-Weierstrass points on Kuribayashi quartics, I (with two parameters)

Abstract

In this paper, we classify the 1-Weierstrass points of the Kuribayashi quartic curves with two parameters $a$ and $b$ defined by the equation \[C_{a,b}:x^{4}+y^{4}+z^{4}+ax^{2}y^{2}+b(x^{2}+y^{2})z^{2}=0,\] such that $(a^2-4)(b^2-4)(a^2-1)(b^2-a-2)\ne 0.$ Furthermore, the geometry of these points is investigated.

16 pages, LaTeX file, Presented in "International Conference on Mathematics, Trends, Development (ICMTD12)" held at Cairo, Egypt, December 27-29, 2012. MSC 2010:Primary 14H55, 14R20; Secondary 14H37, 14H45, 14H50 (References have been modified, proofs have been added, conclusions have been extended,...etc)