Computational Aspects of Hyperelliptic Curves

Details Computational Aspects of Hyperelliptic Curves Computational Aspects of Hyperelliptic Curves

2006-01-17

arxiv.org/abs/math/0601399v1

Computer mathematics, 248--257, Lecture Notes Ser. Comput., 10, World Sci. Publishing, River Edge, NJ, 2003

Mathematics

Algebraic Geometry

Scientific paper

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 $L$.

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