Mutations of splitting maximal modifying modules: The case of reflexive polygons
Abstract
It is known that every three dimensional Gorenstein toric singularity has a crepant resolution. Although it is not unique, all 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 that all 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.
Keywords
Cite
@article{arxiv.1601.05203,
title = {Mutations of splitting maximal modifying modules: The case of reflexive polygons},
author = {Yusuke Nakajima},
journal= {arXiv preprint arXiv:1601.05203},
year = {2019}
}
Comments
50 pages, including many figures, v4: corrected the proof of Lemma 3.7, v3: revised several places, especially subsection 5.6, v2: minor changes