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Rigid Gorenstein toric Fano varieties arising from directed graphs

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


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