论文标题
通过$ a $的重建代数的重建代数同时解决ARTIN组件和同时解决
The Artin Component and Simultaneous Resolution via Reconstruction Algebras of Type $A$
论文作者
论文摘要
本文通过仅使用相应的重建代数的颤动来恢复环状表面奇异性的变形空间的Artin组分，使用非Gorenstein奇点的非交通分辨率来构建经典的变形空间。然后将重建代数的关系变形，变形关系以及GIT商的变化达到同时解决。 This extends work of Brieskorn, Kronheimer, Grothendieck, Cassens-Slodowy and Crawley-Boevey-Holland into the setting of singularities $\mathbb{C}^2/H$ with $H\leq\mathrm{GL}(2,\mathbb{C})$, and furthermore gives a prediction for what is true more generally.
This paper uses noncommutative resolutions of non-Gorenstein singularities to construct classical deformation spaces, by recovering the Artin component of the deformation space of a cyclic surface singularity using only the quiver of the corresponding reconstruction algebra. The relations of the reconstruction algebra are then deformed, and the deformed relations together with variation of the GIT quotient achieve the simultaneous resolution. This extends work of Brieskorn, Kronheimer, Grothendieck, Cassens-Slodowy and Crawley-Boevey-Holland into the setting of singularities $\mathbb{C}^2/H$ with $H\leq\mathrm{GL}(2,\mathbb{C})$, and furthermore gives a prediction for what is true more generally.
