论文标题
在椭圆形的Grothendieck-Springer分辨率的次置切片上
On subregular slices of the elliptic Grothendieck-Springer resolution
论文作者
论文摘要
在\ cite {davis19}中，作者构建了grothendieck-springer的椭圆版本，用于堆栈$ \ mathrm {bun mathrm {bun} _g $ principal bundles的简单连接的简单组$ g $ g $ g $ g $。这是从$ \ mathrm {bun} _g $转到可分离$ g $捆绑的粗模量空间和单个二叠纪点的粗模量空间的结合的地图的同时记录分辨率。在本文中，我们研究了来自该椭圆形的Grothendieck-Springer分辨率的近规则切片的奇异性，分辨率和变形。更确切地说，我们每次$ g $构造了$ \ mathrm {bunrm {bun} _g $的显式切片。对于$ g \ neq sl_2 $，我们描述了椭圆形的grothendieck-springer分辨率的回调，作为混凝土品种，扩展并完善了I. Grojnowski和N. Shepherd-Barron的早期工作，他们将这些品种与del pezzo corper of type $ e $ e $ $ e $相关。我们使用分辨率来识别次规则切片的不稳定基因座的奇异性，并证明扩展的粗模量空间图提供了带有适当重量的圆环 - 依然变形之间的变形。
In \cite{davis19}, the author constructed an elliptic version of the Grothendieck-Springer resolution for the stack $\mathrm{Bun}_G$ of principal bundles under a simply connected simple group $G$ on an elliptic curve $E$. This is a simultaneous log resolution of a map from $\mathrm{Bun}_G$ to the union of the coarse moduli space of semistable $G$-bundles and a single stacky point. In this paper, we study singularities, resolutions and deformations coming from subregular slices of this elliptic Grothendieck-Springer resolution. More precisely, we construct explicit slices of $\mathrm{Bun}_G$ through all subregular unstable bundles, for every $G$. For $G \neq SL_2$, we describe the pullbacks of the elliptic Grothendieck-Springer resolution to these slices as concrete varieties, extending and refining earlier work of I. Grojnowski and N. Shepherd-Barron, who related these varieties to del Pezzo surfaces in type $E$. We use the resolutions to identify the singularities of the unstable locus of the subregular slices, and prove that that the extended coarse moduli space map gives deformations that are miniversal among torus-equivariant deformations with appropriate weights.
