On some constructions of Calabi-Yau manifolds.

• Other Authors: Chan, Kwok Wai.
• Format: Others
• Language: English; Chinese
• Published: 2004
• Subjects: Calabi-Yau manifolds
• Online Access: http://library.cuhk.edu.hk/record=b5891854; http://repository.lib.cuhk.edu.hk/en/item/cuhk-324723

Chan Kwok Wai. === Thesis (M.Phil.)--Chinese University of Hong Kong, 2004. === Includes bibliographical references (leaves 78-81). === Abstracts in English and Chinese. === Chapter 1 --- Introduction to Toric Geometry --- p.7 === Chapter 1.1 --- Definitions of Toric Varieties --- p.7 === Chapter 1.2 --- Properties of Toric Varieties --- p.11 === Chapter 1.2.1 --- Smoothness --- p.12 === Chapter 1.2.2 --- Compactness --- p.12 === Chapter 1.2.3 --- Stratification --- p.13 === Chapter 1.3 --- Divisors on Toric Varieties --- p.14 === Chapter 1.3.1 --- Weil divisors --- p.14 === Chapter 1.3.2 --- Cartier divisors --- p.14 === Chapter 1.4 --- Polarized Toric Varieties --- p.16 === Chapter 2 --- Calabi-Yau Manifolds from Toric Varieties --- p.19 === Chapter 2.1 --- Toric Fano Varieties --- p.19 === Chapter 2.2 --- Calabi-Yau Hypersurf aces in Toric Fano Varieties --- p.23 === Chapter 2.3 --- Computation of Hodge Numbers of Zf --- p.28 === Chapter 2.3.1 --- The results of Danilov and Khovanskii --- p.29 === Chapter 2.3.2 --- "The Hodge number hn-2,1(Zf)" --- p.31 === Chapter 2.3.3 --- "The Hodge number hl,1(zf)" --- p.32 === Chapter 2.4 --- Calabi-Yau Complete Intersections in Toric Fano Va- rieties --- p.34 === Chapter 3 --- Calabi-Yau Manifolds by Quotients --- p.41 === Chapter 3.1 --- Free Group Actions --- p.41 === Chapter 3.2 --- Crepant Resolutions of Orbifolds --- p.44 === Chapter 3.3 --- Examples From Complex Tori --- p.49 === Chapter 3.4 --- Complex Multiplication and Calabi-Yau Threefolds --- p.51 === Chapter 4 --- Calabi-Yau Manifolds by Coverings --- p.56 === Chapter 4.1 --- Cyclic Coverings --- p.56 === Chapter 4.2 --- Admissible Blow-ups --- p.57 === Chapter 4.3 --- Double Covers of P3 Branched Along Octic Arrang- ments --- p.59 === Chapter 4.4 --- The Euler Number of X --- p.61 === Chapter 4.5 --- The Hodge Numbers of X --- p.65 === Chapter 4.6 --- K3-Fibrations and Modularity --- p.69 === Chapter 0 --- Bibliography --- p.78