Conic divisorial ideals of Hibi rings and their applications to non-commutative crepant resolutions
Conic divisorial ideals of Hibi rings and their applications to non-commutative crepant resolutions
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Hibi环的圆锥除数理想及其在非交换克里普特分辨率中的应用
DOI：
10.1007/s00029-019-0523-6
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发表时间：
2019
期刊：
影响因子：
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通讯作者：
Yusuke Nakajima
中科院分区：
文献类型：
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作者：
Akihiro Higashitani;Yusuke Nakajima
本文研究了由偏序集生成的复曲面环Hibi环的除子理想。我们特别刻画了一类特殊的除数理想，称为圆锥曲线使用相关的偏序集。利用我们对锥除子理想的描述，我们还构造了一个模，给出了多项式环的塞格雷积的一个非交换的临界分解（NCCR）。此外，应用称为变异的操作，我们给出了其他模块，给出了它的NCCR。
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.