This project is maintained by ysykimura
2024年1月11日(木) 17:30~19:00
i-Siteなんば S1 (およびZoomのハイブリッド形式の予定)
Wall-and-chamber structures for algebras associated to toric cDV singularities
A consistent dimer model, which is a bipartite graph described on the real two-torus, provides the quiver with relations as its dual graph. For such a quiver with relations, we can consider the stability condition in the sense of A. King. The space of stability parameters has the wall-and-chamber structure, that is, it is decomposed into chambers separated by walls. One of the properties of interest is that for a stability parameter contained in a chamber, the moduli space of stable representations of the quiver gives a projective crepant resolution of a three-dimensional Gorenstein toric singularity and wall-crossings in the stability space induce the variations of projective crepant resolutions. In this talk, I will focus on a consistent dimer model (and the associated quiver) giving rise to projective crepant resolutions of toric cDV (compound Du Val) singularity. In particular, I will show that zigzag paths of a consistent dimer model control the wall-and-chamber structure and the variations of projective crepant resolutions. This talk is based on the preprint arXiv:2309.16112.