本项目计划研究与有理曲面相关的的 Kronheimer-Nakajima quiver 模空间的几何及代数性质。具体包括：（1）确定并研究包含(-2)曲线的 ADE 型 configurations 的有理曲面上的反自对偶向量丛及其与线丛的 exceptional sequences、tilting bundles 等的关系；（2）确定 Kronheimer-Nakajima 的 quiver 模簇（即模空间）上的稳定性条件及其GIT构造。这一项目计划将有理曲面上的根格结构、exceptional sequences 及 quiver 模空间等综合起来研究，并将深化及拓展 Kronheimer, Nakajima, Rudakov, Bridgeland, Orlov等的深刻工作。

This project plans to study the geometric and algebraic properties of Kronheimer-Nakajima quiver moduli spaces associated with rational surfaces. More concretely, we shall: (1) determine the anti-self-dual vector bundles over rational surfaces with a configurations of (-2) curves of ADE-type, and study their relations with exceptional sequences of line bundles, tilting bundles and so on; (2) give the GIT constructions for the so-called Kronheimer-Nakajima's quiver varieties (i.e., quiver moduli spaces), by studying the related stability conditions. This project will uniformly consider the root lattice structures and the exceptional sequences structures on rational surfaces, together with quiver moduli spaces and so on. This study will develop the deep work of Kronheimer, Nakajima, Rudakov, Bridgeland, Orlov and so on.