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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳榮凱 | zh_TW |
| dc.contributor.advisor | Jungkai Alfred Chen | en |
| dc.contributor.author | 張宏彬 | zh_TW |
| dc.contributor.author | Hung-Pin Chang | en |
| dc.date.accessioned | 2024-07-02T16:21:36Z | - |
| dc.date.available | 2024-07-03 | - |
| dc.date.copyright | 2024-07-02 | - |
| dc.date.issued | 2024 | - |
| dc.date.submitted | 2024-06-27 | - |
| dc.identifier.citation | [AKMW02] Dan Abramovich, Kalle Karu, Kenji Matsuki, and Jarosław Włodarczyk, Torification and factorization of birational maps, J. Amer. Math. Soc. 15 (2002), no. 3, 531–572. MR 1896232
[Bro99] Gavin Brown, Flips arising as quotients of hypersurfaces, Math. Proc. Cambridge Philos. Soc. 127 (1999), no. 1, 13–31. MR 1692523 [CLS11] David A. Cox, John B. Little, and Henry K. Schenck, Toric varieties, Graduate Studies in Mathematics, vol. 124, American Mathematical Society, Providence, RI, 2011. MR 2810322 [Dol03] Igor Dolgachev, Lectures on invariant theory, London Mathematical Society Lecture Note Series, vol. 296, Cambridge University Press, Cambridge, 2003. MR 2004511 [Har77] Robin Hartshorne, Algebraic geometry, Graduate Texts in Mathematics, vol. No. 52, Springer, 1977. MR 463157 [Kaw08] Yujiro Kawamata, Flops connect minimal models, Publ. Res. Inst. Math. Sci. 44 (2008), no. 2, 419–423. MR 2426353 [KM98] János Kollár and Shigefumi Mori, Birational geometry of algebraic varieties, Cambridge Tracts in Mathematics, vol. 134, Cambridge University Press, Cambridge, 1998, With the collaboration of C. H. Clemens and A. Corti, Translated from the 1998 Japanese original. MR 1658959 [Mat02] Kenji Matsuki, Introduction to the Mori program, Universitext, Springer, 2002. MR 1875410 [MFK94] David Mumford, John Fogarty, and Frances Kirwan, Geometric invariant theory, third ed., Ergebnisse der Mathematik und ihrer Grenzgebiete (2) [Results in Mathematics and Related Areas (2)], vol. 34, Springer, 1994. MR 1304906 [Mor85] Shigefumi Mori, On 3-dimensional terminal singularities, Nagoya Math. J. 98 (1985), 43–66. MR 792770 [Muk03] Shigeru Mukai, An introduction to invariants and moduli, japanese ed., Cambridge Studies in Advanced Mathematics, vol. 81, Cambridge University Press, Cambridge, 2003. MR 2004218 [Rei87] Miles Reid, Young person’s guide to canonical singularities, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), Proc. Sympos. Pure Math., vol. 46, Part 1, Amer. Math. Soc., Providence, RI, 1987, pp. 345–414. MR 927963 | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/92866 | - |
| dc.description.abstract | Flip 和 flop 是極小模型理論中非常重要的數學對象。但我們知道的 flip 和 flop 的具體例子卻很稀少。 Brown 使用幾何不變量理論有系統地構造了一系列的 flips：這些flip由 C5 中的超曲面的 GIT 商給出。本論文的主要目的是推廣 Brown 的構造。我們對 C6 中的四維代數簇的 GIT 商所導出的 flip 和 flop 進行了分類。同時，我們也證明了在 n ≥ 7 的時候 Cn 中的四維代數簇的 GIT 商所導出的 flip 和 flop 不會產生新的例子。 | zh_TW |
| dc.description.abstract | Flips and flops play major roles in the minimal model program. However, there are few examples of flips and flops. Brown constructed a series of flips given by the GIT quotient of a hypersurface in C5. The main purpose of this thesis is to extend Brown’s construction. We classified flips and flops which are GIT quotient of complete intersection in C6. We also show that there are no more new examples as GIT quotient of complete intersection in Cn with n≥7. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2024-07-02T16:21:36Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2024-07-02T16:21:36Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 致謝 iii
摘要 v Abstract vii Contents ix List of Figures xi List of Tables xiii Chapter 1 Introduction 1 Chapter 2 GIT construction 9 2.1 Geometric invariant theory . . . . . . . . . . . . . . . . . . . . . . . 9 2.2 Construction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11 Chapter 3 Numerical conditions 15 3.1 Contraction condition . . . . . . . . . . . . . . . . . . . . . . . . . . 16 3.2 Intersection condition . . . . . . . . . . . . . . . . . . . . . . . . . . 19 3.3 Singularity condition . . . . . . . . . . . . . . . . . . . . . . . . . . 19 Chapter 4 Hypersurface 27 4.1 Flips for hypersurface (Brown’s case) . . . . . . . . . . . . . . . . . 27 4.2 Flops for hypersurface . . . . . . . . . . . . . . . . . . . . . . . . . 28 Chapter 5 Codimension 2 33 5.1 Examples . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 5.2 Weight type (+, +, −, −, 0, 0; 0, 0) . . . . . . . . . . . . . . . . . . . 36 5.3 Weight type (+, +, +, −, −, 0; +, 0) . . . . . . . . . . . . . . . . . . 38 5.4 The rest weight types . . . . . . . . . . . . . . . . . . . . . . . . . . 50 Chapter 6 Higher codimension 63 6.1 Codimension greater than 3 . . . . . . . . . . . . . . . . . . . . . . 63 6.2 Codimesion 3 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 Chapter 7 Discussions 71 References 73 | - |
| dc.language.iso | en | - |
| dc.subject | 雙有理幾何 | zh_TW |
| dc.subject | 代數幾何 | zh_TW |
| dc.subject | 極小模型理論 | zh_TW |
| dc.subject | 奇異點 | zh_TW |
| dc.subject | 幾何不變量理論 | zh_TW |
| dc.subject | Geometric Invariant Theory | en |
| dc.subject | terminal singularity | en |
| dc.subject | flop | en |
| dc.subject | flip | en |
| dc.subject | Minimal Model Program | en |
| dc.subject | birational geometry | en |
| dc.subject | algebraic geometry | en |
| dc.title | 用幾何不變量理論構造flip以及flop | zh_TW |
| dc.title | Flips and Flops Constructed by GIT Quotient | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 112-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 林學庸;陳俊成;賴青瑞 | zh_TW |
| dc.contributor.oralexamcommittee | Hsueh-Yung Lin;Jiun-Cheng Chen;Ching-Jui Lai | en |
| dc.subject.keyword | 代數幾何,雙有理幾何,極小模型理論,幾何不變量理論,奇異點, | zh_TW |
| dc.subject.keyword | algebraic geometry,birational geometry,Minimal Model Program,flip,flop,terminal singularity,Geometric Invariant Theory, | en |
| dc.relation.page | 74 | - |
| dc.identifier.doi | 10.6342/NTU202401352 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2024-06-28 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 數學系 | - |
| 顯示於系所單位： | 數學系 | |
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