On superelliptic curves of level n and their quotients
I-AIMS paper 2011-2 · Published in Albanian J. Math. 5 (2011), 115–137 · 2011
We study families of superelliptic curves with fixed automorphism groups. Such families are parametrized with invariants expressed in terms of the coefficients of the curves. Algebraic relations among such invariants determine the lattice of inclusions among the loci of superelliptic curves and their field of moduli. We give a Maple package of how to compute the normal form of a superelliptic curve and its invariants. A complete list of all superelliptic curves of genus g ≤ 10 defined over any field of characteristic ≠ 2 is given in a subsequent paper.
MSC classes: 14H32, 14H37, 14K25