Rigid Gorenstein toric Fano varieties arising from directed graphs

• Kara, Selvi ^[1] ; Portakal, Irem ^[3] ; Tsuchiya, Akiyoshi ^[2]
  1. [1] University of Utah

     University of Utah

     Estados Unidos

     
  2. [2] University of Tokyo

     University of Tokyo

     Japón

     
  3. [3] Max-Planck-Institut für Mathematik in den Naturwissenschaften, Inselstrasse 22, 04103, Leipzig, Germany

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• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 74, Fasc. 2, 2023, págs. 333-351
• Idioma: inglés
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• Resumen

  • A directed edge polytope {\mathcal {A}}_G is a lattice polytope arising from root system A_n and a finite directed graph G. If every directed edge of G belongs to a directed cycle in G, then {\mathcal {A}}_G is terminal and reflexive, that is, one can associate this polytope to a Gorenstein toric Fano variety X_G with terminal singularities. It is shown by Totaro that a toric Fano variety which is smooth in codimension 2 and {\mathbb {Q}}-factorial in codimension 3 is rigid. In the present paper, we classify all directed graphs G such that X_G is a toric Fano variety which is smooth in codimension 2 and {\mathbb {Q}}-factorial in codimension 3.