In this note we discuss techniques for determining the automorphism group of a genus $g$ hyperelliptic curve $\X_g$ defined over an algebraically closed field $k$ of characteristic zero. The first technique uses the classical $GL_2 (k)$-invariants of binary forms. This is a practical method for curves of small genus, but has limitations as the genus… (More)
We introduce a new approach of computing the automorphism group and the field of moduli of points p = [C] in the moduli space of hyperel-liptic curves Hg. Further, we show that for every moduli point p ∈ Hg(L) such that the reduced automorphism group of p has at least two involu-tions, there exists a representative C of the isomorphism class p which is… (More)
The development of computational techniques in the last decade has made possible to attack some classical problems of algebraic geometry. In this survey, we briefly describe some open problems related to algebraic curves which can be approached from a computational viewpoint.