Hyperelliptic Curves with Many Automorphisms
Nicolas M\"uller, Richard Pink
TL;DR
This paper classifies complex hyperelliptic curves with a high number of automorphisms and identifies which of their jacobians possess complex multiplication, advancing understanding of their symmetries and algebraic properties.
Contribution
It provides a complete classification of hyperelliptic curves with many automorphisms and characterizes the complex multiplication of their jacobians.
Findings
All such hyperelliptic curves are classified.
Criteria for jacobians to have complex multiplication are established.
The relationship between automorphisms and complex multiplication is clarified.
Abstract
We determine all complex hyperelliptic curves with many automorphisms and decide which of their jacobians have complex multiplication.
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