On Reconstructing Configurations of Points in ${\mathbb P}^2$ from a Joint Distribution of Invariants

Mireille Boutin; Gregor Kemper

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On Reconstructing Configurations of Points in ${\mathbb P}^2$ from a Joint Distribution of Invariants

Mireille Boutin·Gregor Kemper

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Abstract

Consider the diagonal action of the projective group $\PGL_3$ on $n$ copies of ${\mathbb P}^2$. In addition, consider the action of the symmetric group $Σ_n$ by permuting the copies. In this paper we find a set of generators for the invariant field of the combined group $Σ_n \times \PGL_3$. As the main application, we obtain a reconstruction principle for point configurations in ${\mathbb P}^2$ from their sub-configurations of five points. Finally, we address the question of how such reconstruction principles pass down to subgroups.

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Mireille Boutin, Gregor Kemper. 2004-05-16. On Reconstructing Configurations of Points in ${\mathbb P}^2$ from a Joint Distribution of Invariants. https://arxiv.org/abs/math/0405313

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