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Primes and order structure in the product spaces

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Abstract

Aprime of a product spaceS (in particular: a Segre variety) is a proper subsetH of the point set ofS, such that any line either is contained inH or meetsH in exactly one point. In contrast to what happens for the Grassmann varieties [1], in the Segre varieties there are primes which are not hyperplane sections. Some of such primes “destroy” the order structure. This is a consequence of the description of the primes that we give in this paper. On the other hand, it is not possible to give an intrinsic characterization of all hyperplane sections. So, we consider some special ones among them, that we call “singular primes”, which allow a satisfactory study of the order structure of the product spaces.

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Authors and Affiliations

  1. Dip. di Metodi e Modelli Matematici, Università di Roma “La Sapienza”, Via A. Scarpa 16, I-00161, Roma, Italy

    Alessandro Bichara

  2. Dip. di Matematica Pura ed Applicata, Università di Padova, Via Belzoni 7, I-35131, Padova, Italy

    Corrado Zanella

  3. Institut für Mathematik, Universität Hannover, Postfach 6009, D-30060, Hannover, Germany

    Jürgen Misfeld

Authors
  1. Alessandro Bichara
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  2. Jürgen Misfeld
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  3. Corrado Zanella
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Additional information

A. Bichara and C. Zanella dedicate this work to the other co-author Mr. J. Misfeld, who sadly died on 6th January 1995.

The research reported in this paper has been supported by a grant of theVigoni Program.

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Bichara, A., Misfeld, J. & Zanella, C. Primes and order structure in the product spaces. J Geom 58, 53–60 (1997). https://doi.org/10.1007/BF01222926

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  • DOI: https://doi.org/10.1007/BF01222926

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