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

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

2004-05-16

arxiv.org/abs/math/0405313v1

Mathematics

Commutative Algebra

Scientific paper

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 $\Sigma_n$ by permuting the copies. In this paper we find a set of generators for the invariant field of the combined group $\Sigma_n \times \PGL_3$. 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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