论文标题
组合Reid的一致二聚体模型的食谱
Combinatorial Reid's recipe for consistent dimer models
论文作者
论文摘要
里德（Reid）有限的Abelian子组$ g \ subset \ text {sl}（3，\ mathbb {c}）$的配方是一个组合过程，标志着$ G $ -HILBERT方案的福利粉丝，其不可偿还的表示为$ G $。 Logvinenko等人后来证明了cautis--logvinenko的几何mckay对应猜想，该cautis--logvinenko描述了$ g \ text {-hilb} $的派生类别中的某些对象。我们通过与Bocklandt-Craw-craw-Quintero-vélez的几何对应度相吻合的方式来将Reid的配方推广到任何一致的二聚体模型。我们的主要工具将Nakamura的拼图转换为一致的二聚体模型。
Reid's recipe for a finite abelian subgroup $G\subset \text{SL}(3,\mathbb{C})$ is a combinatorial procedure that marks the toric fan of the $G$-Hilbert scheme with irreducible representations of $G$. The geometric McKay correspondence conjecture of Cautis--Logvinenko that describes certain objects in the derived category of $G\text{-Hilb}$ in terms of Reid's recipe was later proved by Logvinenko et al. We generalise Reid's recipe to any consistent dimer model by marking the toric fan of a crepant resolution of the vaccuum moduli space in a manner that is compatible with the geometric correspondence of Bocklandt--Craw--Quintero-Vélez. Our main tool generalises the jigsaw transformations of Nakamura to consistent dimer models.
