It is conjectured that the SYZ map equals to the inverse mirror map. In dimension two this conjecture is proved, and in dimension three supporting evidences of the equality are studied in various examples. Since the SYZ map is expressed in terms of open Gromov-Witten invariants, this conjectural equality established an enumerative meaning of the inverse mirror map. / Moreover a computational method of open Gromov-Witten invariants for toric Calabi-Yau manifolds is invented. As an application, the Landau-Ginzburg mirrors of compact semi-Fano toric surfaces are computed explicitly. / This thesis gives a procedure to carry out SYZ construction of mirrors with quantum corrections by Fourier transform of open Gromov-Witten invariants. Applying to toric Calabi-Yau manifolds, one obtains the Hori-Iqbel-Vafa mirror together with a map from the Kahler moduli to the complex moduli of the mirror, called the SYZ map. / Lau, Siu Cheong. / Adviser: N.C. Leung. / Source: Dissertation Abstracts International, Volume: 73-06, Section: B, page: . / Thesis (Ph.D.)--Chinese University of Hong Kong, 2011. / Includes bibliographical references (leaves 143-148). / 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, [201-] System requirements: Adobe Acrobat Reader. Available via World Wide Web. / Abstract also in Chinese.
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_344847 |
| Date | January 2011 |
| Contributors | Lau, Siu Cheong., 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 (148 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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