标题： 环面的格罗滕迪克-斯普林格映射 显示英文标题

标题： Toroidal analogues of the Grothendieck-Springer map

摘要： 我们研究非交换规则曲面在轨道曲线上的导出范畴中的对象的模空间，以找到框架层在等变椭圆曲面上的模空间的等变变形。 这些导出范畴是预投射代数的模范畴和曲线上的扭曲D-模范畴的共同推广。 我们证明了等变椭圆曲面上点的希尔伯特方案的双有理几何由椭圆根系控制，并在一般情况下提出猜想并在特殊情况下证明，这些导出范畴中的对象的模空间为希尔伯特方案的双有理模型提供了变形。 我们还研究了这种变形在中心纤维的几何表示理论中的应用，特别是产生几何对应关系，从而在中心纤维的等变上同调上产生李代数作用，并给出了关于单值群的Namikawa-Markman Weyl群的反射作用的公式。 显示英文摘要

摘要： We study moduli spaces of objects in the derived category of noncommutative ruled surfaces over orbifold curves to find equivariant deformations of moduli spaces of framed sheaves on equivariant elliptic surfaces. These derived categories are a common generalization of the category of modules of the preprojective algebra and of the category of twisted D-modules over a curve. We show that the birational geometry of the Hilbert scheme of points on an equivariant elliptic surface is controlled by an elliptic root system, and conjecture in general and prove in special cases that moduli spaces of objects in these derived categories provides a deformation of birational models for the Hilbert scheme. We also study the applications of this deformation to the geometric representation theory of the central fiber, specifically to produce geometric correspondences giving rise to Lie algebra actions on the equivariant cohomology of the central fiber and give formulas for the action of the Namikawa-Markman Weyl group of monodromy reflections in terms of this Lie algebra.