Geometric Reid's recipe for dimer models
Geometric Reid's recipe for dimer models
复制标题
几何里德的二聚体模型配方
DOI：
10.1007/s00208-014-1085-8
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发表时间：
2014
影响因子：
1.4
通讯作者：
Bocklandt R
中科院分区：
文献类型：
--
作者：
Bocklandt R
三维环面Gorenstein奇点的Crepant决议推导出等价于非交换代数所产生的一致二聚体模型。通过选择一个特殊的稳定性参数，从而一个杰出的crepant决议，这导出的等价推广的Fourier-Mukai变换有关的希尔伯特计划和斜群代数的有限交换子群。我们表明，这种等价发送的顶点单纯纯层，除了零顶点映射到的对偶复杂的紧凑的例外轨迹。这概括了Cautis-Logvinenko（J Reine Angew Math 636：193-236，2009）和Cautis-Craw-Logvinenko（J Reine Angew Math arXiv：1205.3110 ，2014）到二聚体设置，尽管我们的方法在每种情况下是不同的。我们还明确地描述了这些纯层中的一些，并计算了其余部分的支持度，提供了Logvinenko（J Algebra 324：2064-2087，2010）结果的二聚体模型模拟。
Crepant resolutions of three-dimensional toric Gorenstein singularities are derived equivalent to noncommutative algebras arising from consistent dimer models. By choosing a special stability parameter and hence a distinguished crepant resolution, this derived equivalence generalises the Fourier-Mukai transform relating the-Hilbert scheme and the skew group algebrafor a finite abelian subgroup of. We show that this equivalence sends the vertex simples to pure sheaves, except for the zero vertex which is mapped to the dualising complex of the compact exceptional locus. This generalises results of Cautis–Logvinenko (J Reine Angew Math 636:193–236, 2009) and Cautis–Craw–Logvinenko (J Reine Angew Math arXiv:1205.3110 , 2014) to the dimer setting, though our approach is different in each case. We also describe some of these pure sheaves explicitly and compute the support of the remainder, providing a dimer model analogue of results from Logvinenko (J Algebra 324:2064–2087, 2010).