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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 林惠雯(Hui-Wen Lin) | |
| dc.contributor.author | Ching-Peng Huang | en |
| dc.contributor.author | 黃景芃 | zh_TW |
| dc.date.accessioned | 2021-06-16T13:34:53Z | - |
| dc.date.available | 2013-07-30 | |
| dc.date.copyright | 2013-07-30 | |
| dc.date.issued | 2013 | |
| dc.date.submitted | 2013-07-18 | |
| dc.identifier.citation | [1] CAIB ˘AR, Mirel. Minimal models of canonical 3-fold singularities and their Betti numbers.
International Mathematics Research Notices, 2005, vol. 2005, no 26, p. 1563-1581. [2] CHEN, Jhih-Bin ; On crepant resolution of some hypersurface singularities. MA Thesis, Na- tional Central University, 2004. [3] COX, David A., LITTLE, John B., et SCHENCK, Henry K. Toric varieties. American Math- ematical Soc., 2011. [4] DANILOV, Vladimir Ivanovich. Birational geometry of toric 3-folds. Mathematics of the USSR-Izvestiya, 1983, vol. 21, no 2, p. 269. [5] DOLGACHEV, Igor Weighted projective spaces. Group actions and vector fields, Lecture Notes in Math., vol. 956, Springer-Verlag, 1982, pp. 34-71. [6] FLETCHER, A. R. Working with weighted complete intersections. Max-Planck-Inst. f. Math- ematik, 1989. [7] HAYAKAWA, Takayuki. Blowing ups of 3-dimensional terminal singularities. Publications of the Research Institute for Mathematical Sciences, 1999, vol. 35, no 3, p. 515-570. [8] HODGE, William V. D., et PEDOE, Daniel 1994. Methods of algebraic geometry. Cambridge (GB): Cambridge university press. [9] KOLL ’AR, J’anos et MORI, Shigefumi. Classification of three-dimensional flips. Journal of the American Mathematical Society, 1992, vol. 5, no 3, p. 533-703. [10] KOLL ’AR, J’anos et MORI, Shigefumi. Birational geometry of algebraic varieties. Cam- bridge University Press, 2008. [11] LIN, Hui-Wen Combinatorial method in adjoint linear systems on toric varieties. Michigan Math. J. 51 (2003), no. 3, 491501. [12] MATSUKI, Kenji. Introduction to the Mori program. Universitext, Springer- Verlag, New York, 2002. [13] MORI, Shigefumi. On 3-dimensional terminal singularities. Nagoya Mathematical Jour- nal, 1985, vol. 98, p. 43-66. [14] REID, Miles. Canonical 3-folds, in Journ’ees de g’eom’etrie alg’ebrique d’Angers, ed. A. Beauville, Sijthoff and Noordhoff, Alphen 1980, 273–310. [15] REID, Miles. Decomposition of toric morphisms. Arithmetic and geometry, Vol.II, 395418, Progr. Math., 36 , Birkh‥auser Boston, MA, 1983. [16] REID, Miles. Minimal models of canonical 3-folds, in Advanced studies in Pure Math. 1, Analytic varieties and algebraic varieties, ed. S. Iitaka, Kinokuniya and North-Holland, 1983, 131–180. [17] REID, Miles. Young person’s guide to canonical singularities, in Algebraic Geometry, Bow- doin 1985, ed. S. Bloch, Proc. of Symposia in Pure Math. 46, A.M.S. (1987), vol. 1, 345– 414. [18] REID, Miles. The Du Val singularities An; Dn; E6; E7; E8. www.warwick.ac.uk/ ˜masda/surf/more/DuVal.pdf [19] REID, Miles. Surface cyclic quotient singularities and Hirzebruch Jung resolutions. homepages.warwick.ac.uk/˜masda/surf/more/cyclic.pdf | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/62224 | - |
| dc.description.abstract | 本文根據 Miles Reid 及森重文等人的研究，探討三維 canonical 奇異點的理論，主要著重於三維 terminal 奇異點的分類；並於附錄中研習 toric morphism 的分解，以助於瞭解 toric 幾何中 terminal 奇異點所扮演的角色。 | zh_TW |
| dc.description.abstract | Based on the work of Miles Reid, I would like to survey the
theory of 3-dimensional canonical singularities in this article. I mainly concentrate on the classification of 3-dimensional terminal singularities. Also, in the appendix, I study the decomposition of toric morphisms in order to know the role of terminal singularities played in the Minimal Model Program for toric varieties. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T13:34:53Z (GMT). No. of bitstreams: 1 ntu-102-R00221008-1.pdf: 464686 bytes, checksum: 3a848f9af9c19a1756fed21e87b1434a (MD5) Previous issue date: 2013 | en |
| dc.description.tableofcontents | 1. Introduction 1
1.1. Definitions and conventions 2 1.2. Definition of canonical singularities 2 1.3. Hyperquotient singularities 2 1.4. Overview of the article 3 2. Reductions 5 2.1. Reduction to terminal singularities 5 2.2. Using toric techniques 9 2.3. The terminal lemma and its proof 14 3. Classification of 3-dimensional terminal singularities 22 3.1. First steps 23 3.2. The cA case 26 3.3. The odd case 29 3.4. The cD-E case 30 3.5. Further results 34 Appendix A. Decomposition of toric morphisms 34 A.1. Contraction of extremal rays 34 A.2. Flipping 37 A.3. The canonical divisor 38 References 41 | |
| dc.language.iso | en | |
| dc.subject | canonical 奇異點 | zh_TW |
| dc.subject | terminal 奇異點 | zh_TW |
| dc.subject | 三維 variety | zh_TW |
| dc.subject | toric MMP | zh_TW |
| dc.subject | terminal MMP | en |
| dc.subject | 3-fold | en |
| dc.subject | terminal singularity | en |
| dc.subject | canonical singularity | en |
| dc.title | 三維 canonical 奇異點理論的探討 | zh_TW |
| dc.title | A Discussion on the Theory of 3-dimensional Canonical Singularities | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 101-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 王金龍(Chin-Lung Wang),李元斌(Yuan-Pin Lee) | |
| dc.subject.keyword | 三維 variety,canonical 奇異點,terminal 奇異點,toric MMP, | zh_TW |
| dc.subject.keyword | 3-fold,canonical singularity,terminal singularity,terminal MMP, | en |
| dc.relation.page | 41 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2013-07-18 | |
| 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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