Self-dual projective toric varieties and their ideals

• Thoma, Apostolos ^[1] ; Vladoiu, Marius ^[2]
  1. [1] University of Ioannina

     University of Ioannina

     Dimos Ioánnina, Grecia

     
  2. [2] University of Bucharest

     University of Bucharest

     Sector 3, Rumanía

     
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 77, Fasc. 1, 2026, págs. 99-116
• Idioma: inglés
• DOI: 10.1007/s13348-024-00459-3
• Texto completo no disponible (Saber más ...)
• Resumen

  • We describe explicitly all multisets of weights whose defining projective toric varieties are self-dual. In addition, we describe a remarkable and unexpected combinatorial behaviour of the defining ideals of these varieties. The toric ideal of a self-dual projective variety is weakly robust, that means the Graver basis is the union of all minimal binomial generating sets. When, in addition, the self-dual projective variety is defined by a non-pyramidal configuration, then the toric ideal is strongly robust, namely the Graver basis is a minimal generating set, therefore there is only one minimal binomial generating set which is also a reduced Gröbner basis with respect to every monomial order and thus, equals the universal Gröbner basis.

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