On the Hilbert function of lines union one non-reduced point

• Enrico Carlini ^[1] ; Maria Virginia Catalisano ^[2] ; Anthony V. Geramita ^[3]
  1. [1] Polytechnic University of Turin

     Polytechnic University of Turin

     Torino, Italia

     
  2. [2] University of Genoa

     University of Genoa

     Genoa, Italia

     
  3. [3] Queen's University

     Queen's University

     Canadá

     

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• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 15, Nº Extra 1 (Special volume), 2016, págs. 69-84
• Idioma: inglés
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• Resumen

  • In this paper we consider the problem of determining the Hilbert function of schemes X ⇢ Pn which are the generic union of s lines and one mmultiple point. We completely solve this problem for any s and m when n " 4.

    When n = 3 we find several defective such schemes and conjecture that they are the only ones. We verify this conjecture in several cases.