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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳榮凱 | |
| dc.contributor.author | Yen-An Chen | en |
| dc.contributor.author | 陳延安 | zh_TW |
| dc.date.accessioned | 2021-05-15T17:55:21Z | - |
| dc.date.available | 2014-07-29 | |
| dc.date.available | 2021-05-15T17:55:21Z | - |
| dc.date.copyright | 2014-07-29 | |
| dc.date.issued | 2014 | |
| dc.date.submitted | 2014-07-15 | |
| dc.identifier.citation | [Abh56] S. S. Abhyankar, Local uniformization on algebraic surfaces over ground fields of characteristic p neq 0, Ann. of Math. (2) 63 (1956), 491–526.
[Abh66] S. S. Abhyankar, Resolution of singularities of embedded algebraic surfaces, Pure and Applied Mathematics, Vol. 24, Academic Press, New York-London, 1966. [BCHM10] C. Birkar, P. Cascini, C. D. Hacon, and J. McKernan, Existence of minimal models for varieties of log general type, J. Amer. Math. Soc. 23 (2010), no. 2, 405–468. [Che13] J. A. Chen, Explicit resolution of three dimensional terminal singularities, arXiv preprint arXiv:1310.6445 (2013). [CP08] V. Cossart and O. Piltant, Resolution of singularities of threefolds in positive characteristic. I. Reduction to local uniformization on Artin-Schreier and purely inseparable coverings, J. Algebra 320 (2008), no. 3, 1051–1082. [CP09] V. Cossart and O. Piltant, Resolution of singularities of threefolds in positive characteristic. II, J. Algebra 321 (2009), no. 7, 1836–1976. [CTX13] P. Cascini, H. Tanaka, and C. Xu, On base point freeness in positive characteristic, arXiv preprint arXiv:1305.3502 (2013). [FJ74] G. Frey and M. Jarden, Approximation theory and the rank of abelian varieties over large algebraic fields, Proc. London Math. Soc. (3) 28 (1974), 112–128. [Fuj84] T. Fujita, Fractionally logarithmic canonical rings of algebraic surfaces, Journal of the Faculty of Science, The University of Tokyo, Sect. 1 A, Mathematics 30 (1984), no. 3, 685–696. [Ful93] W. Fulton, Introduction to toric varieties, Annals of Mathematics Studies, vol. 131, Princeton University Press, Princeton, NJ, 1993, The William H. Roever Lectures in Geometry. [Har77] R. Hartshorne, Algebraic geometry, Springer-Verlag, New York-Heidelberg, 1977, Graduate Texts in Mathematics, No. 52. [Hir64] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero. I, II, Ann. of Math. (2) 79 (1964), 109–203; ibid. (2) 79 (1964), 205–326. [HW02] N. Hara and K. Watanabe, F-regular and F-pure rings vs. log terminal and log canonical singularities, J. Algebraic Geom. 11 (2002), no. 2, 363–392. [HX13] C. D. Hacon and C. Xu, On the three dimensional minimal model program in positive characteristic, arXiv preprint arXiv:1302.0298 (2013). [Kee99] S. Keel, Basepoint freeness for nef and big line bundles in positive characteristic, Ann. of Math. (2) 149 (1999), no. 1, 253–286. [KM08] J. Koll ́ar and S. Mori, Birational geometry of algebraic varieties, vol. 134, Cambridge University Press, 2008. [KMM87] Y. Kawamata, K. Matsuda, and K. Matsuki, Introduction to the minimal model problem, Advanced Studies in Pure Math. 10(1987) 10 (1987), 283– 360. [KSB88] J. Koll ́ar and N. I. Shepherd-Barron, Threefolds and deformations of surface singularities, Invent. Math. 91 (1988), no. 2, 299–338. [Mat02] K. Matsuki, Introduction to the Mori program, Springer, 2002. [Mor85] S. Mori, On 3-dimensional terminal singularities, Nagoya Math. J. 98 (1985), 43–66. [Ray78] M. Raynaud, Contre-exemple au “vanishing theorem” en caracte ́ristique p > 0, C. P. Ramanujam—a tribute, Tata Inst. Fund. Res. Studies in Math., vol. 8, Springer, Berlin-New York, 1978, pp. 273–278. [Rei83] M. Reid, Minimal models of canonical 3-folds, Algebraic varieties and analytic varieties (Tokyo, 1981), Adv. Stud. Pure Math., vol. 1, North-Holland, Amsterdam, 1983, pp. 131–180. [Rei87] M. Reid, Young person’s guide to canonical singularities, Algebraic geometry, Bowdoin, 1985 (Brunswick, Maine, 1985), Proc. Sympos. Pure Math., vol. 46, Amer. Math. Soc., Providence, RI, 1987, pp. 345–414. [Sho86] V. V. Shokurov, The nonvanishing theorem, Mathematics of the USSR- Izvestiya 26 (1986), no. 3, 591–604. [Tan12] H. Tanaka, Minimal models and abundance for positive characteristic log surfaces, arXiv preprint arXiv:1201.5699 (2012). | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/5298 | - |
| dc.description.abstract | 本文分為兩個部分。第一個部分介紹極小模型理論是如何運作的，尤其是在正特徵數的時候。第二個部分，Mori 在特徵數零時對三維 terminal 奇點的分類中，我確定了大部分在正特徵數時，仍然會是 terminal 奇點。 | zh_TW |
| dc.description.abstract | In this thesis, there are two parts. The first part is to introduce what the minimal model program (MMP) is and how it works, especially in positive characteristic. Also, I illustrate some differences between characteristic zero and positive characteristic. In the second part, I verify that the classification Mori gave in characteristic zero for the terminal singularities in dimension 3 is mostly true in positive characteristic. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-15T17:55:21Z (GMT). No. of bitstreams: 1 ntu-103-R01221007-1.pdf: 11268199 bytes, checksum: 72f04f29ee29f8d5f6cd12bc829268b5 (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 Abstract iv Contents v List of Figures vii 1. What is MMP ? 1 1.1 Classification ................................ 1 1.2 What is a minimal model? ......................... 2 1.3 Asymptotic Riemann-Roch Theorem.................... 2 2. MMP in characteristic zero 4 2.1 Surface case................................. 4 2.2 Higher dimensional case .......................... 8 3. MMP in positive characteristic 13 3.1 Differences with characteristic zero .................... 13 3.2 F-Singularities................................ 15 3.3 MMP for surfaces.............................. 21 3.4 MMP for 3-folds .............................. 24 4. Resolution for terminal singularities 26 4.1 Characteristic zero ............................. 27 4.2 Cyclic quotient singularities in positive characteristic . . . . . . . . . . . 28 4.2.1 Toric varieties............................ 28 4.2.2 Cyclic quotients .......................... 29 4.3 cAn type singularities............................ 30 4.3.1 n=1................................ 32 4.3.2 n≥2................................ 33 4.3.3 Termination............................. 35 4.4 cA/r type singularities ........................... 38 4.5 cAx/2 and cD type singularities ...................... 40 4.5.1 Settings............................... 40 4.5.2 The base case............................ 42 4.5.3 Inductive step............................ 45 Bibliography 50 | |
| dc.language.iso | en | |
| dc.subject | 極小模型理論 | zh_TW |
| dc.subject | terminal 奇點 | zh_TW |
| dc.subject | 正特徵數 | zh_TW |
| dc.subject | Terminal Singularity | en |
| dc.subject | Minimal Model Program | en |
| dc.subject | Positive Characteristic | en |
| dc.title | 正特徵數中的極小模型理論 | zh_TW |
| dc.title | Minimal Model Program in Positive Characteristic | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 102-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳俊成,章源慶 | |
| dc.subject.keyword | 極小模型理論,正特徵數,terminal 奇點, | zh_TW |
| dc.subject.keyword | Minimal Model Program,Positive Characteristic,Terminal Singularity, | en |
| dc.relation.page | 52 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2014-07-15 | |
| 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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| ntu-103-1.pdf | 11 MB | Adobe PDF | 檢視/開啟 |
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