Wong, Tak Pui. / Thesis (M.Phil.)--Chinese University of Hong Kong, 2007. / Includes bibliographical references (leaves 60-62). / Abstracts in English and Chinese. / Table of Contents --- p.ii / Abstract --- p.iii / Acknowledgements --- p.iv / Chapter 0 --- Introduction --- p.1 / Chapter 1 --- Definitions of Plane Tropical Curves --- p.4 / Chapter 1.1 --- Motivation --- p.4 / Chapter 1.2 --- As Varieties over the Field of Puiseux Series --- p.7 / Chapter 1.3 --- As Varieties over the Tropical Semiring --- p.10 / Chapter 1.4 --- A Combinatorial Description of Plane Tropical Curves --- p.16 / Chapter 2 --- Properties of Plane Tropical Curves --- p.21 / Chapter 2.1 --- The Degree-genus Formula --- p.21 / Chapter 2.2 --- Bezout's Theorem --- p.24 / Chapter 3 --- Non-Archimedean Amoebas and Patchworking Method --- p.28 / Chapter 3.1 --- Computing Amoebas --- p.28 / Chapter 3.2 --- Patchworking Method --- p.37 / Chapter 3.2.1 --- Maslov's Dequantization --- p.37 / Chapter 3.2.2 --- Patchworking Method --- p.39 / Chapter 4 --- Mikhalkin's Correspondence Theorem --- p.41 / Chapter 4.1 --- Parameterized Plane Tropical Curves --- p.41 / Chapter 4.2 --- Statement of the Main Theorem --- p.43 / Chapter 4.3 --- Lattice Paths --- p.46 / Chapter 4.4 --- Complex Tropical Curves --- p.51 / Chapter 4.5 --- Sketch Proof of the Main Theorem --- p.54 / Chapter 4.5.1 --- Proof of Lemma 1 --- p.55 / Chapter 4.5.2 --- Proof of Lemma 2 --- p.56 / Bibliography --- p.60
| Identifer | oai:union.ndltd.org:cuhk.edu.hk/oai:cuhk-dr:cuhk_326085 |
| Date | January 2007 |
| Contributors | Wong, Tak Pui., 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, bibliography |
| Format | print, iv, 62 leaves : ill. ; 30 cm. |
| 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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