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| 研究生： |
康立信 Kang, Li Xin |
|---|---|
| 論文名稱： |
三維熱帶幾何之研究 On Three Dimensional Tropical Geometry |
| 指導教授： | 蔡炎龍 |
| 學位類別： |
碩士
Master |
| 系所名稱： |
理學院 - 應用數學系 Department of Mathematical Sciences |
| 論文出版年： | 2007 |
| 畢業學年度： | 95 |
| 語文別： | 英文 |
| 論文頁數： | 54 |
| 中文關鍵詞： | 熱帶幾何 |
| 相關次數： | 點閱：127 下載：90 |
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在這篇論文裡,我們主要在探討熱帶幾何的基本性質並研究熱帶幾何近來的發展,特別是Mikhalkin計算曲線個數的方法.最後,我們簡短的討論熱帶幾何在三維的一些情況.
In this thesis, we study the properties of tropical geometry and survey the recent development of tropical geometry, especially Mikhalkin's method of counting curves. We also briefly study tropical geometry in three-dimensional case.
1.Introduction-----------------------------------p.1
2.Motivation-------------------------------------p.3
3.Properties of Tropical Geometry----------------p.27
4.The Application: Enumerative Geometry----------p.36
5.Tropical Geometry in R3------------------------p.49
1.Statistics of frameworks and motions of panel structures,a projective geometry introduction.
2.Tropical algebraic geometry.(Gathmann)
3.Welschinger invariant and enumeration of real rational curves.
4.Tropical algebraic geometry.(Itenberg)
5.First steps in tropical geometry.
6.Counting plane curves of any genus.
7.Non-archimedean amoebas and tropical varieties.
8.Gromov-witten classes, quantum cohomology and enumerative geometry.
9.Rational tropical curves in Rn.
10.Amoebas of algebraic varieties and tropical geometry.
11.Enumerative tropical algebraic geometry in R2.
12.Patchworking singular algebraic curves, non-archimedean amoebas, and enumerative geometry.
13.Dequantization of real algebraic geometry on logarithmic paper.
14.Spinor states of real rational curves in real algebraic convex 3-manifolds and enumerative invariants.
15.Invariant of real rational symplectic 4-manifolds and lower bounds in real enumerative geometry.