Polynomial Invariants of the Heisenberg Group with extra Symmetries

Abstract

Let $G\subset SO(4)$ denote a finite subgroup containing the Heisenberg group. In these notes we classify all these 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 ${\mathbb{P}}_3$ which we started in math. AG/0106080. It turns out that we have five more pencils, two of them containing surfaces with nodes.

29 pages, 1 figure

References in corpus (1)

• Polyhedral Groups and Pencils of K3-Surfaces with Maximal Picard Number