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Rational surfaces, simple Lie algebras and flat G bundles over elliptic curves. / CUHK electronic theses & dissertations collection

It is well-known that del Pezzo surfaces of degree 9 -- n. are in one-to-one correspondence to flat En bundles over elliptic curves which are anti-canonical curves of such surfaces. In my thesis, we study a broader class of rational surfaces which are called ADE surfaces. We construct Lie algebra bundles of any type on these surfaces, and extend the above correspondence to flat G bundles over elliptic curves, where G is a simple, compact and simply-connected Lie group of any type. Concretely, we establish a natural identification between the following two very different moduli spaces for a Lie group G of any type: the moduli space of rational surfaces with G-configurations and the moduli space of flat G-bundles over a fixed elliptic curve. / Zhang, Jiajin. / "July 2007." / Adviser: Leung Nai Chung Conan. / Source: Dissertation Abstracts International, Volume: 69-01, Section: B, page: 0357. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (p. 77-79). / Electronic reproduction. Hong Kong : Chinese University of Hong Kong, [2012] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Electronic reproduction. [Ann Arbor, MI] : ProQuest Information and Learning, [200-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstracts in English and Chinese. / School code: 1307.

Identiferoai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_343983
Date January 2007
ContributorsZhang, Jiajin., Chinese University of Hong Kong Graduate School. Division of Mathematics.
Source SetsThe Chinese University of Hong Kong
LanguageEnglish, Chinese
Detected LanguageEnglish
TypeText, theses
Formatelectronic resource, microform, microfiche, 1 online resource (79 p. : ill.)
RightsUse 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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