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Mutations of splitting maximal modifying modules: The case of reflexive polygons

Research paper by Yusuke Nakajima

Indexed on: 20 Apr '16Published on: 20 Apr '16Published in: Mathematics - Representation Theory



Abstract

It is known that every three dimensional Gorenstein toric singularity has a crepant resolution. Although it is not unique, any crepant resolutions are connected by repeating the operation "flop". On the other hand, this singularity also has a non-commutative crepant resolution (= NCCR) which is constructed from a consistent dimer model. Such an NCCR is given as the endomorphism ring of a certain module which we call splitting maximal modifying module. In this paper, we show any splitting maximal modifying modules are connected by repeating the operation "mutation" of splitting maximal modifying modules for the case of toric singularities associated with reflexive polygons.