D-膜上的Azumaya结构和锥的变形与分解：Klebanov-Strassler-Witten vs. Polchinski-Grothendieck
Azumaya structure on D-branes and deformations and resolutions of a conifold revisited: Klebanov-Strassler-Witten vs. Polchinski-Grothendieck
摘要：
在[L-Y1]、[L-L-S-Y]和[L-Y2]（分别为arXiv：0709.1515 [math.AG]、arXiv：0809.2121 [math.AG]和arXiv：0901.0342 [math.AG]）的续篇中，我们从D-膜上的Azumaya结构和环面几何的角度研究了锥状结构上的D-膜探测。给出了如何通过Azumaya点的态射获得标准复曲面二次曲面$Y$的变形和分辨率的细节。这应该与Klebanov和Witten [K-W]（arXiv：hep-th/9807080）以及Klebanov和Strasser [K-S]（arXiv：hep-th/0007191）的工作中通过D膜探针观察圆锥体的变形和分辨率的量子场论/D膜图像进行比较。最后给出了与非交换去奇异分解的比较。
英文摘要：
In this sequel to [L-Y1], [L-L-S-Y], and [L-Y2] (respectively arXiv:0709.1515 [math.AG], arXiv:0809.2121 [math.AG], and arXiv:0901.0342 [math.AG]), we study a D-brane probe on a conifold from the viewpoint of the Azumaya structure on D-branes and toric geometry. The details of how deformations and resolutions of the standard toric conifold $Y$ can be obtained via morphisms from Azumaya points are given. This should be compared with the quantum-field-theoretic/D-brany picture of deformations and resolutions of a conifold via a D-brane probe sitting at the conifold singularity in the work of Klebanov and Witten [K-W] (arXiv:hep-th/9807080) and Klebanov and Strasser [K-S] (arXiv:hep-th/0007191). A comparison with resolutions via noncommutative desingularizations is given in the end.
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