Gale对偶与非交换奇点解消的线性化映射
Gale duality and the linearisation map for noncommutative crepant resolutions
AI总结：
本文用几何方法描述了三维非交换奇点解消的箭图模空间上线性化映射的Gale对偶，并利用一对整值矩阵表述Reid配方，为相关猜想提供了新证据。
摘要：
我们用几何术语描述了三维非交换奇点解消相关的箭图模空间上线性化映射的Gale对偶映射。这使我们能够在此背景下用一对整值矩阵来表述Reid配方，其中一个矩阵似乎满足引人注目的符号相干性质。我们为一个在环面情形已知成立的猜想提供了新的证据，该猜想断言：由自同构丛的行列式之间的极小生成关系集编码了导出等价下顶点单模的像的支集，反之亦然。
英文摘要：
We describe in geometric terms the map that is Gale dual to the linearisation map for quiver moduli spaces associated to noncommutative crepant resolutions in dimension three. This allows us to formulate Reid's recipe in this context in terms of a pair of integer-valued matrices, one of which appears to satisfy an attractive sign-coherence property. We provide some new evidence for a conjecture, known to hold in the toric case, which implies that a minimal generating set of relations between the determinants of the tautological bundles encodes the supports of the images of the vertex simples under the derived equivalence, and vice-versa.
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