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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳榮凱(Jung-Kai Chen) | |
| dc.contributor.author | Wei-Che Cheng | en |
| dc.contributor.author | 鄭偉哲 | zh_TW |
| dc.date.accessioned | 2021-06-16T08:14:51Z | - |
| dc.date.available | 2014-03-21 | |
| dc.date.copyright | 2014-03-21 | |
| dc.date.issued | 2014 | |
| dc.date.submitted | 2014-02-13 | |
| dc.identifier.citation | Brown, G. , Flips arising as quotients of hypersurfaces. Math. Proc. Cambridge Philos. Soc. { f 127} (1999), no. 1, 13--31.
avid Cox, John Little, Hal Schenck Toric Varieties 2010, American Mathematical Society Press. Ch.11 Fulton, W. , Introduction to Toric Varieties, Princeton Univ. Press. p. 35 Danilov, V. , Birational Geometry of Toric 3-folds , 1983, Math. USSR Izv., 21 ,269-280 Igor V. Dolgachev, Lectures on Invariant Theory, 2003, Igor V. Dolgachev, Weighted Projective Varieties; in Group actions and Vector Fields, 1981, Proc. Vancouver, SLN extbf{956} ,34-71 R. Hartshorne, Algebraic Geometry, 1977, New York: Springer-Verlag J. Koll'ar and S. Mori, Birational geometry of algebraicvarieties, 1998, Cambridge Univ. Press. K. Matsuki, Introduction to the Mori Program, 2002, Springer-Verlag New York, Inc. Press. p.318 H. Kraft, P. Slodowy, T.A. Springer(editors), Algebraic Transformation Groups, , DMV Seminar,Bd. 13, Brikh'auser Verlag, 1989 Koll'ar, J and Shepard-Barron, N. , Threefolds and Deformation of Surface Singularities , 1988, Inv. Math. , 299-338. Morrison, D. and Steven, G. , Terminal Quotient Singularities in Dimension Three and Four , 1984, Proc. Amer. Math. Soc., 15-20 Mori, S. , On 3-dimensional Terminal Singularities , 1985, Nagoya Math. J. 43-66. S.Mukai, An Introduction to Invariants and Moduli, 2003, Cambridge Univ. Press. Miles Reid Surface cyclic quotient singularities and Hirzebruch-Jung resolutions Reid, M. , Minimal Models of Canonical Threefolds , 1983, Algebraic Varieties and Analytic Varieties, Adv. Stud. Pure Math. 131-180 | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/58429 | - |
| dc.description.abstract | Minimal Model Program(MMP) 是近代複代數幾何中發展相當活躍的一個領域，它指出每一個僅含有terminal singularity的複投影代數簇X總能夠在其雙有理類之中找到一個“最小的”X’來做為代表，尋找這個最小代表角色的方法是透過構造一連串的映射X→…→X’。這是S.Mori在80年代的工作。
在這一連串的映射中，為了確保找到minimal model，我們可能會遇到一種叫做flip的數學現象。我們必須要對flip有充分的了解，但事實上數學界對於flip的例子所知甚少。G.Brown提出了一種對於flip的構造方法，基本上是透過幾何不變理論(Geometric Invariant Theory, GIT)的知識來構造flip。G.Brown本人也分類了所有在五維複空間中的超曲面所能構造的flip。本篇論文將要介紹初步的GIT知識以及G.Brown所提出的構造，並在文末給初幾個flip的例子。 | zh_TW |
| dc.description.abstract | Flips is a special phenomenon in birational geometry. When we run minimal model program to a projective variety X which has only terminal singularities, one might consider another candidate on which the canonical divisor is relative ample. This would lead the concept of flips. People known little about flips. In this note, we give a construction of flips suggested from G.Brown and give some examples of flips from this construction. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T08:14:51Z (GMT). No. of bitstreams: 1 ntu-103-R00221007-1.pdf: 446025 bytes, checksum: 91d93743633a2a7b6803d7797564d0ae (MD5) Previous issue date: 2014 | en |
| dc.description.tableofcontents | 口試委員會審定書---i
誌謝---ii 中文摘要---iii 英文摘要---1 第一章 Introduction---1 第二章 Geometric Invariant Theory---2 2.1 Definition of quotients---2 2.2 Linear reductiveiy---3 2.3 Algebraic group acting on an affine variety---4 2.4 Algebraic group acting on an quasi-projective variety---6 2.5 Quotient when variety is not affine---9 第三章 Classification of 3-dimensional terminal singularities---10 第四章 The construction of flipping diagram and 3-dimensional classification---11 4.1 Construction---11 4.2 3-dimensional classification from G.Brown---14 第五章 Examples---17 參考文獻---25 | |
| dc.language.iso | zh-TW | |
| dc.subject | Minimal Model Program | zh_TW |
| dc.subject | birational geometry | zh_TW |
| dc.subject | flip | zh_TW |
| dc.subject | terminal singularity | zh_TW |
| dc.subject | Geometric Invariant Theory | zh_TW |
| dc.title | 以幾何不變理論構造flip之方法 | zh_TW |
| dc.title | A Construction of Flips via GIT Theory | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 102-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳俊成(Jiun-Cheng Chen),江謝宏任(Hung-Jen Chiang-Hsieh),余正道(Jeng-Daw Yu),莊武諺(Wu-Yen Chuang) | |
| dc.subject.keyword | Minimal Model Program,birational geometry,flip,terminal singularity,Geometric Invariant Theory, | zh_TW |
| dc.relation.page | 25 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2014-02-13 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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