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Modernity of Halphen’s variations on a theme of Monge

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Abstract

We construct a \(\mathbb {Z}\)/3\(\mathbb {Z}\)-slice to the natural action of \({ PGL}(V)\) on the variety of smooth arcs in the projective space \(\mathbb {P}(V)\).

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Acknowledgments

The second author is grateful to Abdelghani El Mazouni, who wrote [2], which is an analysis of Halphen’s thesis [5], for very useful discussions relevant to the subject of the present paper.

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Authors and Affiliations

  1. Equipe de géométrie, U.M.R. 7502 du CNRS, Institut Elie Cartan, Université de Lorraine, BP 239, Vandoeuvre-les-Nancy Cedex, 54506, Nancy, France

    Caroline Gruson

  2. LMV, Université de Versailles, 45 avenue des Etats-Unis, 78035, Versailles cedex, France

    Laurent Gruson

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  1. Caroline Gruson
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  2. Laurent Gruson
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Correspondence to Laurent Gruson.

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Dedicated to P. Ellia.

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Gruson, C., Gruson, L. Modernity of Halphen’s variations on a theme of Monge. Rend. Circ. Mat. Palermo, II. Ser 66, 83–95 (2017). https://doi.org/10.1007/s12215-016-0268-4

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  • DOI: https://doi.org/10.1007/s12215-016-0268-4

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