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 / Chapter 2.1 --- Standard representations --- p.16 / Chapter 2.2 --- Minuscule representations --- p.17 / Chapter 2.3 --- Configurations of ( -1)-curves --- p.17 / Chapter 2.4 --- Minuscule representations from ( -1)-curves --- p.19 / Chapter 2.5 --- Bundles from ( -1)-curves --- p.21 / Chapter 2.6 --- Outline of Proofs for g ≠E₈ --- p.22 / Chapter 3 --- A[subscript n] case --- p.24 / Chapter 3.1 --- A[subscript n] standard representation bundle Lη^(An,Cn+1) --- p.24 / Chapter 3.2 --- An Lie algebra bundle Sη^(An) --- p.28 / Chapter 3.3 --- An minuscule representation bundle Lη^(An,^kCn+1) --- p.28 / Chapter 4 --- Dn case --- p.30 / Chapter 4.1 --- Dn standard representation bundle Lη^(Dn;C2n) --- p.30 / Chapter 4.2 --- Dn Lie algebra bundle Sη^(Dn) --- p.34 / Chapter 4.3 --- Dn spinor representation bundles Lη^(Dn;S±06) --- p.34 / Chapter 5 --- En case --- p.39 / Chapter 5.1 --- E₆ case --- p.39 / Chapter 5.2 --- E₇ case --- p.42 / Chapter 5.3 --- E₈ case --- p.44 / Chapter 6 --- Proof of Theorem 1.2.1 --- p.45 / Chapter II --- Affine ADE bundles --- p.50 / Chapter 7 --- Affine ADE Lie algebra bundles --- p.51 / Chapter 7.1 --- Affine ADE curves --- p.51 / Chapter 7.2 --- Affine ADE bundles --- p.53 / Chapter 8 --- Trivialization of E₀ gover Ci's after deformations --- p.57 / Chapter 8.1 --- Trivializations in loop ADE cases --- p.58 / Chapter 8.2 --- Trivializations in affine ADE cases --- p.60 / Chapter 8.3 --- Proof (except the loop E₈ case) --- p.60 / Chapter 8.4 --- Proof for the loop E₈ case --- p.62 / Chapter III --- Deformability --- p.65 / Chapter 9 --- En-bundle over Xn with n≤9 --- p.66 / Chapter 9.1 --- En-bundle over Xn with n ≤ 9 --- p.66 / Chapter 9.2 --- Deformability of such E₀E₈ --- p.68 / Chapter 9.3 --- Negative curves in X9 --- p.70 / Chapter 9.4 --- Proof of Theorems 9.2.1 and 9.2.2 --- p.75 / Chapter A --- Minuscule configurations --- p.78 / Chapter B --- A ffine Lie algebras --- p.80
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_328136 |
| Date | January 2013 |
| Contributors | Chen, Yunxia., Chinese University of Hong Kong Graduate School. Division of Mathematics. |
| Source Sets | The Chinese University of Hong Kong |
| Language | English, Chinese |
| Detected Language | English |
| Type | Text, bibliography |
| Format | electronic resource, electronic resource, remote, 1 online resource (87 leaves) |
| Rights | Use of this resource is governed by the terms and conditions of the Creative Commons “Attribution-NonCommercial-NoDerivatives 4.0 International” License (http://creativecommons.org/licenses/by-nc-nd/4.0/) |
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