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
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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.