We give an explicit description of a non-normal irreducible
subvariety of the moduli space of Riemann surfaces of genus $3$
characterized by a non-cyclic group action. Defining equations of
a family of curves representing non-normal points of this
subvariety are computed. We also find defining equations of the
family of hyperelliptic curves of genus $3$ whose full
automorphism group is $C_2\times C_4$. This completes the list of
full automorphism groups of hyperelliptic curves.
@article{1098885439,
author = {Cirre, Francisco Javier},
title = {On a subvariety of the moduli space},
journal = {Rev. Mat. Iberoamericana},
volume = {20},
number = {1},
year = {2004},
pages = { 953-960},
language = {en},
url = {http://dml.mathdoc.fr/item/1098885439}
}
Cirre, Francisco Javier. On a subvariety of the moduli space. Rev. Mat. Iberoamericana, Tome 20 (2004) no. 1, pp. 953-960. http://gdmltest.u-ga.fr/item/1098885439/