Set-theoretic complete intersections on binomials, the simplicial toric case

• Barile, Margherita ^[2] ; Morales, Marcel ^[3] ; Thoma, Apostolos ^[1]
  1. [1] University of Ioannina

     University of Ioannina

     Dimos Ioánnina, Grecia

     
  2. [2] Dipartimento di Matematica, Universitá degli Studi di Bari, Via Orabona 4, 70125 Bari (Italy)
  3. [3] Université de Grenoble I, lnstitut Fourier, URA 188, B.P. 74, 38402 Saint-Martin D'Heres Cedex, and IUFM de Lyon, 5 rue Anselme, 69317 Lyon Cedex (France)

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• Localización: Pesquimat, ISSN-e 1609-8439, ISSN 1560-912X, Vol. 3, Nº. 2, 2000
• Idioma: inglés
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• Resumen

  • Let V be a simplicial toric variety of codimension r over a field of any characteristic. We completely characterize the implicial toric varieties that are set-theoretic complete intersections on binomials. In particular we prove that: 1. In characteristic zero, V is a set-theoretic complete intersection on binomials if and only jf V is a. complete intersection.  Moreover, if F1,…,Fr; are binomials such that I(V)= rad( F1, . .. ,Fr), th en I(V) = (F1, ... ,Fr). We also get a geometric proof of some of the results in [9] characterizing complete intersections by gluing; semigroups. 2. In positive characteristic p, V is a set-theoretic complete intersection on binomials if and only if V is complete 1y p-glued. These results improve and complete all known results on these topics.