Determining equations of families of cyclic curves

Abstract

In previous work we determined automorphism groups of cyclic algebraic curves defined over fields of any odd characteristic. In this paper we determine parametric equations of families of curves for each automorphism group for such curves.

arXiv comment5 Tables

References in corpus (5)

• The locus of curves with prescribed automorphism group
• Some special families of hyperelliptic curves
• Thetanulls of cyclic curves of small genus
• Determining the automorphism group of a hyperelliptic curve
• On the automorphism groups of some AG-codes based on $C_{a,b}$ curves

Cited by in corpus (11)

• From hyperelliptic to superelliptic curves
• Bielliptic curves of genus 3 in the hyperelliptic moduli
• On Jacobians of curves with superelliptic components
• Superelliptic curves with many automorphisms and CM Jacobians
• On The Group Algebra Decomposition of a Jacobian Variety
• The case for superelliptic curves
• Cyclic curves over the reals
• Genus 3 hyperelliptic curves with (2, 4, 4)-split Jacobians
• Generalized superelliptic Riemann surfaces
• On the automorphism groups of some AG-codes based on $C_{a,b}$ curves
• Heights on algebraic curves