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arXiv · 1702.07058

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

Akihiro Higashitani·Yusuke Nakajima
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Abstract

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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BibTeXRIS

Akihiro Higashitani, Yusuke Nakajima. 2017-02-23. Conic divisorial ideals of Hibi rings and their applications to non-commutative crepant resolutions. https://arxiv.org/abs/1702.07058

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