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Conic divisorial ideals of Hibi rings and their applications to non-commutative crepant resolutions. (English) Zbl 1437.13022
Summary: 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.
MSC:
13C14 Cohen-Macaulay modules
06A11 Algebraic aspects of posets
14M25 Toric varieties, Newton polyhedra, Okounkov bodies
16S38 Rings arising from noncommutative algebraic geometry
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