We study mirror symmetry via Fourier-Mukai-type transformations, which we call SYZ mirror transformations, in view of the ground-breaking Strominger-Yau-Zaslow Mirror Conjecture which asserted that the mirror symmetry for Calabi-Yau manifolds could be understood geometrically as a T-duality modified by suitable quantum corrections. We apply these transformations to investigate a case of mirror symmetry with quantum corrections, namely the mirror symmetry between the A-model of a toric Fano manifold X¯ and the B-model of a Landau-Ginzburg model (Y, W). Here Y is a noncompact Kahler manifold and W : Y → C is a holomorphic function. We construct an explicit SYZ mirror transformation which realizes canonically the isomorphism QH*X&d1; ≅Ja cW between the quantum cohomology ring of X¯ and the Jacobian ring of the function W. We also show that the symplectic structure oX¯ of X¯ is transformed to the holomorphic volume form eWOY of ( Y, W). Concerning the Homological Mirror Symmetry Conjecture, we exhibit certain correspondences between A-branes on X¯ and B-branes on (Y, W) by applying the SYZ philosophy. / Chan, Kwok Wai. / Adviser: Nai Chung Conan Leung. / Source: Dissertation Abstracts International, Volume: 70-06, Section: B, page: 3536. / Thesis (Ph.D.)--Chinese University of Hong Kong, 2008. / Includes bibliographical references (leaves 52-56). / 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.
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_344267 |
| Date | January 2008 |
| Contributors | Chan, Kwok Wai., 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, theses |
| Format | electronic resource, microform, microfiche, 1 online resource (vii, 56 leaves : ill.) |
| 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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