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Conic divisorial ideals of Hibi rings and their applications to non-commutative crepant resolutions

  • Akihiro Higashitani [1] ; Yusuke Nakajima [2]
    1. [1] Osaka University

      Osaka University

      Kita Ku, Japón

    2. [2] University of Tokyo

      University of Tokyo

      Japón

  • Localización: Selecta Mathematica, New Series, ISSN 1022-1824, Vol. 25, Nº. 5, 2019
  • Idioma: inglés
  • DOI: 10.1007/s00029-019-0523-6
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  • Resumen
    • In this paper, we study divisorial ideals of a Hibi ring which is a toric ring arising from a partially ordered set. We especially characterize the special class of divisorial ideals called conic using the associated partially ordered set. Using our description of conic divisorial ideals, we also construct a module giving a non-commutative crepant resolution (NCCR) of the Segre product of polynomial rings. Furthermore, applying the operation called mutation, we give other modules giving NCCRs of it.


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