Polynomial Invariants of the Heisenberg Group with extra Symmetries

Details Polynomial Invariants of the Heisenberg Group with extra Symmetries Polynomial Invariants of the Heisenberg Group with extra Symmetries

2003-03-28

arxiv.org/abs/math/0303364v1

Mathematics

Algebraic Geometry

29 pages, 1 figure

Scientific paper

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.

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