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On Reconstructing Configurations of Points in ℙ2 from a Joint Distribution of Invariants

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Applicable Algebra in Engineering, Communication and Computing Aims and scope

Abstract.

Consider the diagonal action of the projective group PGL3 on n copies of ℙ2. 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 ×PGL3. As the main application, we obtain a reconstruction principle for point configurations in ℙ2 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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Authors and Affiliations

  1. Department of Mathematics, Purdue University, 150 N. University St., West Lafayette, IN, 47907, USA

    Mireille Boutin

  2. Technische Universität München, Zentrum Mathematik - M11, Boltzmannstrasse 3, 85748, Garching, Germany

    Gregor Kemper

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  1. Mireille Boutin
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  2. Gregor Kemper
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Correspondence to Mireille Boutin.

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Boutin, M., Kemper, G. On Reconstructing Configurations of Points in ℙ2 from a Joint Distribution of Invariants. AAECC 15, 361–391 (2005). https://doi.org/10.1007/s00200-004-0168-2

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  • DOI: https://doi.org/10.1007/s00200-004-0168-2

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