Geometry and computation of 2-Weierstrass points on Kuribayashi quartic curves. (English) Zbl 1202.14032
Summary: We study the geometry of the 2-Weierstrass points on the Kuribayashi quartic curves
\[ C_a: x^4+y^4+z^4+ a(x^2y^2+y^2z^2+x^2z^2)= 0 \quad (a\neq 1,\pm2). \]
The 2-Weierstrass points on \(C_a\) are divided into flexes and sextactic points. It is known that the symmetric group \(S_4\) acts on \(C_a\). Using the \(S_4\)-action, we classify the 2-Weierstrass points on \(C_a\).
\[ C_a: x^4+y^4+z^4+ a(x^2y^2+y^2z^2+x^2z^2)= 0 \quad (a\neq 1,\pm2). \]
The 2-Weierstrass points on \(C_a\) are divided into flexes and sextactic points. It is known that the symmetric group \(S_4\) acts on \(C_a\). Using the \(S_4\)-action, we classify the 2-Weierstrass points on \(C_a\).
MSC:
| 14H55 | Riemann surfaces; Weierstrass points; gap sequences |
| 14H10 | Families, moduli of curves (algebraic) |
