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Sur les hypersurfaces dont les sections hyperplanes sont à module constant

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The Grothendieck Festschrift

Part of the book series: Progress in Mathematics ((MBC))

Résumé

Cette note a pour origine une question de L. Illusie (motivée par [I]): quelles sont les hypersurfaces dont toutes les sections hyperplanes lisses sont isomorphes entre elles? La réponse est très simple: outre les hyper-quadriques, ce sont (à un isomorphisme projectif près) les hypersurfaces d’équation \(\sum T_i^{q + 1} = 0\), où q est une puissance de la caractéristique.

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Bibliographie

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Author information

Authors and Affiliations

  1. Université Paris-Sud, Orsay, France

    Arnaud Beauville

Authors
  1. Arnaud Beauville
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Editor information

Editors and Affiliations

  1. Institut des Hautes Études Scientifiques, F-91440, Bures-sur-Yvette, France

    Pierre Cartier

  2. Département de Mathématiques, Université de Paris-Sud, F-91405, Orsay, France

    Luc Illusie  & Gérard Laumon  & 

  3. Department Mathematics, Princeton University, 08544, Princeton, NJ, USA

    Nicholas M. Katz

  4. Max-Planck Institut für Mathematik, D-53111, Bonn, Germany

    Yuri I. Manin

  5. Department of Mathematics, University of California, 94720, Berkeley, CA, USA

    Kenneth A. Ribet

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Beauville, A. (2007). Sur les hypersurfaces dont les sections hyperplanes sont à module constant. In: Cartier, P., Illusie, L., Katz, N.M., Laumon, G., Manin, Y.I., Ribet, K.A. (eds) The Grothendieck Festschrift. Progress in Mathematics. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-0-8176-4574-8_5

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