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Computational Aspects of Hyperelliptic Curves

Research paper by Tanush Shaska

Indexed on: 16 Jan '06Published on: 16 Jan '06Published in: Mathematics - Algebraic Geometry



Abstract

We introduce a new approach of computing the automorphism group and the field of moduli of points $\p=[C]$ in the moduli space of hyperelliptic curves $\H_g$. Further, we show that for every moduli point $\p \in \H_g(L)$ such that the reduced automorphism group of $\p$ has at least two involutions, there exists a representative $C$ of the isomorphism class $\p$ which is defined over $L$.