论文标题
迈向borel矩图的仿射和几何不变理论商
Towards the affine and geometric invariant theory quotients of the Borel moment map
论文作者
论文摘要
我们研究Borel力矩图$μ_b：t^*（\ Mathfrak {b} \ times \ Mathbb {C}^n）\ rightArrow \ rightarrow \ Mathfrak {b}^*$，由$（r，s，s，i，i，j）\ mapsto [r，s]+ij+ij+ij+gitients n gengorth ge ge ngients cointient $μ_b^{ - 1}（0）/\！\！/_ {\ det} b $和$μ_b^{ - 1}（0）/\！\！/_ {\！我们还提供了$ 2^n $不可约为$μ_b$的奇异基因座的见解。最后，类似于希尔伯特（Hilbert） - 梳理形态，我们讨论了Borel设置的GIT商是奇异性的解决方案。
We study the Borel moment map $μ_B:T^*(\mathfrak{b}\times \mathbb{C}^n)\rightarrow \mathfrak{b}^*$, given by $(r,s,i,j)\mapsto [r,s]+ij$, and describe our algorithm to construct the geometric invariant theory (GIT) quotients $μ_B^{-1}(0)/\!\!/_{\det}B$ and $μ_B^{-1}(0)/\!\!/_{\det^{-1}}B$, and the affine quotient $μ_B^{-1}(0)/\!\!/B$. We also provide an insight of the singular locus of $2^n$ irreducible components of $μ_B$. Finally, analogous to the Hilbert--Chow morphism, we discuss that the GIT quotient for the Borel setting is a resolution of singularities.
