Non-commutative crepant resolution of minimal nilpotent orbit closures of type A and Mukai flops
Non-commutative crepant resolution of minimal nilpotent orbit closures of type A and Mukai flops
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A 型和 Mukai 触发器的最小幂零轨道闭包的非交换 Crepant 分辨率
DOI：
10.1016/j.aim.2017.08.010
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发表时间：
2017
影响因子：
1.7
通讯作者：
Hara Wahei
中科院分区：
文献类型：
--
作者：
Suekawa M;Fujikawa Y and Esaka M. (Eds. Hossain MA;Munne-Bosch S;Burritt DJ;Vivancos PD;Fujita M and Lorence A);Hara Wahei;Hara Wahei
本文构造了a型最小幂零轨道闭包B(1)的一个非交换褶解（= NCCR），并研究了一个NCCR与B(1)的极小幂零轨道闭包Y、Y+的褶解之间的关系。更确切地说，我们证明了NCCR是具有一定关系的双Beilinson颤振的路径代数同构的，并且我们将B(1)的褶解Y和Y+重构为颤振表示的模空间。我们还研究了基于NCCR的B(1)的渐变决议Y和Y+之间的Kawamata-Namikawa导出的等价性。我们还证明了Y的派生范畴上的p -扭转对应于NCCR的某种操作，我们称之为多突变，而多突变是Iyama-Wemyss突变的组合。
In this article, we construct a non-commutative crepant resolution (= NCCR) of a minimal nilpotent orbit closure B (1)‾ of type A, and study relations between an NCCR and crepant resolutions Y and Y+ of B (1)‾. More precisely, we show that the NCCR is isomorphic to the path algebra of the double Beilinson quiver with certain relations and we reconstruct the crepant resolutions Y and Y+ of B (1)‾ as moduli spaces of representations of the quiver. We also study the Kawamata–Namikawa's derived equivalence between crepant resolutions Y and Y+ of B (1)‾ in terms of an NCCR. We also show that the P-twist on the derived category of Y corresponds to a certain operation of the NCCR, which we call multi-mutation, and that a multi-mutation is a composition of Iyama–Wemyss's mutations.