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Mathematische Annalen

, Volume 364, Issue 3–4, pp 1135–1166 | Cite as

Tissus algébriques exceptionnels

  • Luc Pirio
Article
  • 127 Downloads

Abstract

In (Pirio and Trépreau, Int Math Res Not IMRN, doi: 10.1093/imrn/rnu066, 2014), it has been proved that for \(r > 1, n \ge 2\) and \(d \ge (r +1)(n-1)+2\), a d-web of t ype (rn) with maximal rank is algebraizable in the classical sense, except maybe when \(n \ge 3\) and \(d = (r + 2)(n - 1)+1\). In the present paper, one considers this particular case. Under these hypotheses on n and d, one constructs some examples of ‘exceptional algebraic webs’: these are generalized algebraic webs of maximal rank that are not algebraizable in the classical sense.

Résumé

Dans (Pirio et Trépreau, Int Math Res Not IMRN, doi:10.1093/imrn/rnu066, 2014), nous avons montré que pour \(r>1\), \(n\ge 2\) et \(d\ge (r+1)(n-1)+2\), un d-tissu de type (rn) de rang maximal est algébrisable au sens classique, sauf peut-être lorsque \(n\ge 3\) et \(d= (r+2)(n-1)+1\). On s’intéresse ici à ce cas particulier. Sous ces hypothèses sur n et d, on construit des exemples de “tissus algébriques exceptionnels”: il s’agit de tissus algébriques d’incidence de rang maximal qui ne sont pas algébrisables au sens classique.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  1. 1.IRMAR, UMR 6625 du CNRSCNRS & Université Rennes 1Rennes CedexFrance

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