本申请项目主要研究含有ADE奇点的有理曲面及相关系列的问题，具体包括：（1）含有ADE奇点的del Pezzo曲面的分类和构造，含有ADE奇点的del Pezzo曲面上的E_n向量丛，del Pezzo曲面的family上的E_n向量丛；（2）含有ADE奇点的有理曲面上的李代数向量丛，Brieskorn-Slodowy-Grothendieck图下的伴随ADE向量丛及它们在对应奇异曲面上的限制。这一系列研究将综合考虑并拓展Friedman，Morgan，Witten，Donagi，Slodowy等的深刻工作，并有助于我们更深入的了解代数曲面与李理论之间的联系。

This project plans to study rational surfaces with ADE singularities and some related problems, including: (1) classification and construction of del Pezzo surfaces with ADE singularities, E_n bundles over del Pezzo surfaces with ADE singularities, E_n bundles over a family of del Pezzo surfaces; (2) Lie algebra bundles over rational surfaces with ADE singularities, the associated ADE bundles under Brieskorn-Slodowy-Grothendieck diagram and their restrictions to the corresponding singular surfaces. This study will unify and develop the deep work of Friedman, Morgan, Witten, Donagi, Slodowy and so on. Moreover, this study will be helpful for fully understanding the connection between algebraic surfaces and Lie theory.