Group generated by the Weierstrass points of a plane quartic (Q2759011)

Let \({\mathcal C}\) be a smooth projective curve. The Weierstrass points of \({\mathcal C}\) are the points of inflection of the canonical linear system. The paper under review considers the curve given by the equation \(f=X^4+ Y^4+Z^4+ 3(X^2Y^2+X^2 Z^2+Y^2Z^2)=0\). As a smooth plane quartic its Weierstrass points are the zeros of the Hessian of \(f\). It turns out that \({\mathcal C}\) posseses exactly 12 Weierstrass points, each of weight 2. In the paper the group generated by the Weierstrass points is explicitly described. For this the authors use the Abel-Jacobi embedding of \({\mathcal C}\) and the fact, that the Jacobian of \({\mathcal C}\) is isomorphic to the third power of an elliptic curve.