Strominger-Yau-Zaslow Transformations in mirror symmetry.

• Other Authors: Chan, Kwok Wai.
• Format: Others
• Language: English; Chinese
• Published: 2008
• Subjects: Fourier transformations; Manifolds (Mathematics); Mirror symmetry
• Online Access: http://library.cuhk.edu.hk/record=b6074634; http://repository.lib.cuhk.edu.hk/en/item/cuhk-344267

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.