On a subvariety of the moduli space

Cirre, Francisco Javier

doi:10.4171/RMI/411

Revista Matemática Iberoamericana

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Volume 20, Issue 3, 2004, pp. 953–960

DOI: 10.4171/RMI/411

Published online: 2004-12-31

On a subvariety of the moduli space

Francisco Javier Cirre^[1]

(1) UNED, Madrid, Spain

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.

Keywords: Riemann surface, moduli space, automorphism group

Cirre Francisco Javier: On a subvariety of the moduli space. Rev. Mat. Iberoam. 20 (2004), 953-960. doi: 10.4171/RMI/411