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Polynomial Invariants of the Heisenberg Group with extra Symmetries

Alessandra Sarti
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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.

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Alessandra Sarti. 2003-03-28. Polynomial Invariants of the Heisenberg Group with extra Symmetries. https://arxiv.org/abs/math/0303364

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