ADE and affine ADE bundles over complex surfaces with pg = 0. ; CUHK electronic theses & dissertations collection

我们研究了P[subscript g]=0 的复曲面x 上的ADE 向量丛和仿射ADE 向量丛。 ; 首先，我们假设x 上有一个ADE 奇异点。这个奇异点在极小分解Y 中的例外轨迹是一条相应形式的ADE 曲线。利用这条ADE 曲线和向量丛的扩张，我们构造了Y 上的一个ADE 向量丛，而且这个向量丛可以下降到x上。此外，我们利用Y 上( -1)- 曲线的组合，描述了他们的极小表示向量丛。 ; 其次，我们假设x 是一个椭圆曲面，而且x 上有一个仿射ADE 形式的奇异纤维。类似于以前，我们构造了X 上的一个仿射ADE 向量丛，而且这个向量丛在这条仿射ADE 曲线上的每一个不可约成分上都是平凡的。 ; 然后，当X 是P²上突起n ≤9 个点时, x 上有一个典型的En 向量丛。我们详细的研究了x 的几何和这个E[subscript n] 向量丛的可变形性之间的关系。 ; We study ADE and affine ADE bundles over complex surfaces X with P[subscript g] = 0. ; First, we suppose X admits an ADE singularity. The exceptional locus of this singularity in the minimal resolution Y is an ADE curve of corresponding type. Using this ADE curve and bundle extensions, we construct an ADE bundle over Y which can descend to X. Furthermore, we describe their minuscule representation bundles in terms of configuration of (reducible) (-1)-curves. ; Second, we assume X is an elliptic surface with a singular fiber of affine ADE type. Similar to above studies, we construct the affine ADE bundle over X which is trivial on each irreducible component of the affine ADE curve. ; Third, when X is the blowup of P² at n ≤9 points, there is a canonical E[subscript n] bundle over it. We give a detailed study of the relationship between the geometry of X and the deformability of this bundle. ; Detailed summary in vernacular field only. ; Detailed summary in vernacular field only. ; Detailed summary in vernacular field only. ; Detailed summary in vernacular field only. ; Chen, Yunxia. ; On t.p. "g" is subscript. ; Thesis (Ph.D.)--Chinese University of Hong Kong, 2013. ; Includes bibliographical references (leaves 84-87). ; Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. ; Abstracts also in Chinese. ; Chapter I --- ADE bundles --- p.9 ; Chapter 1 --- ADE Lie algebra bundles --- p.10 ; Chapter 1.1 --- ADE singularities --- p.10 ; Chapter 1.2 --- ADE bundles --- p.12 ; Chapter 2 --- Minuscule representations and ( -1)-curves --- p.16 ...