Symmetric Surfaces with Many Singularities#.

Let G ⊂ SO(4) denote a finite subgroup containing the Heisenberg group. In this paper we classify all such groups, we find the dimension of the spaces of G-invariant polynomials and we give equations for the generators whenever the space has dimension two. Then we complete the study of the corresponding G-invariant pencils of surfaces in [Popf]3 which we started in Sarti [Sarti, A. (2000). Pencils of symmetric surfaces in [Popf]3(C). J. Algebra 246:429–452]. It turns out that we have five more pencils, two of them containing surfaces with nodes. [ABSTRACT FROM AUTHOR]