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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳榮凱(Jungkai Alfred Chen) | |
| dc.contributor.author | Hsin-Ku Chen | en |
| dc.contributor.author | 陳星谷 | zh_TW |
| dc.date.accessioned | 2021-05-12T09:33:52Z | - |
| dc.date.available | 2018-08-18 | |
| dc.date.available | 2021-05-12T09:33:52Z | - |
| dc.date.copyright | 2018-08-18 | |
| dc.date.issued | 2018 | |
| dc.date.submitted | 2018-07-19 | |
| dc.identifier.citation | [Ben85] X. Benveniste, Sur le cone des 1-cycles effectifs en dimension 3, Math. Ann. 272 (1985), 257-265.
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/handle/123456789/1183 | - |
| dc.description.abstract | 這篇論文包含兩個部份。於第一部份我們證明了一個平滑三維多樣體和其極小模型的
貝堤數的差可被該平滑三維多樣體的皮喀數所限制。於第二部份我們證明了任一小平 維度為一的平滑三維多樣體的第九十六個複正則系統會決定其飯高纖維。 | zh_TW |
| dc.description.abstract | This thesis consists of two parts. In the first part we prove that the difference of the Betti numbers of a smooth threefold and its minimal model can be bounded by a constant depending only on the Picard number of the smooth threefold. In the second part we prove that the 96-th pluricanonical system of a smooth threefold of Kodaira dimension one defines the Iitaka fibration. | en |
| dc.description.provenance | Made available in DSpace on 2021-05-12T09:33:52Z (GMT). No. of bitstreams: 1 ntu-107-D02221002-1.pdf: 734015 bytes, checksum: 0b6832ecd7c625f8cedd84f9cf1f1235 (MD5) Previous issue date: 2018 | en |
| dc.description.tableofcontents | 1 Introduction 1
1.1 Convention and notation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2 Algebraic geometric background . . . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.1 Ample, nef and big divisors . . . . . . . . . . . . . . . . . . . . . . . 3 1.2.2 Iitaka fibration and the Kodaira dimension . . . . . . . . . . . . . . . 4 2 Minimal Model Program and Terminal Threefolds 6 2.1 Minimal model program . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1 Minimal model program for surfaces . . . . . . . . . . . . . . . . . . 7 2.1.2 Cone theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 2.1.3 Singularities in minimal model program . . . . . . . . . . . . . . . . . 10 2.1.4 Higher dimensional minimal model program . . . . . . . . . . . . . . 10 2.1.5 Abundance conjecture . . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2 Terminal threefolds . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.2.1 Classification of terminal threefolds . . . . . . . . . . . . . . . . . . . 14 2.2.2 Singular Riemann-Roch formula . . . . . . . . . . . . . . . . . . . . . 15 2.2.3 Weighted blow-up . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16 2.2.4 Divisorial contraction to points . . . . . . . . . . . . . . . . . . . . . . 18 3 Betti numbers in the three dimensional minimal model program 24 3.1 Preliminary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 3.1.1 Biraitonal maps between terminal threefolds . . . . . . . . . . . . . . 25 3.1.2 Topology of terminal threefolds . . . . . . . . . . . . . . . . . . . . . 27 3.2 The estimate on topology . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 3.2.1 The existence of N -constant . . . . . . . . . . . . . . . . . . . . . . . 31 3.2.2 The existence of M -constant . . . . . . . . . . . . . . . . . . . . . . . 41 3.3 The boundedness of Betti numbers . . . . . . . . . . . . . . . . . . . . . . . . 44 3.4 Examples and applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50 4 Threefolds of Kodaira dimension one 55 4.1 Preliminary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57 4.1.1 The canonical bundle formula . . . . . . . . . . . . . . . . . . . . . . 57 4.1.2 Kollár vanishing theorem . . . . . . . . . . . . . . . . . . . . . . . . . 58 4.1.3 Weak positivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 59 4.2 K3 or Enriques fibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60 4.3 Abelian fibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 4.4 Bielliptic fibrations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68 4.5 Boundedness of Iitaka fibration for Kodaira dimension one . . . . . . . . . . . 70 | |
| dc.language.iso | en | |
| dc.subject | 黑肯-瑪柯能猜想 | zh_TW |
| dc.subject | 複三體 | zh_TW |
| dc.subject | 極小模型計劃 | zh_TW |
| dc.subject | 貝堤數 | zh_TW |
| dc.subject | 複正則系統 | zh_TW |
| dc.subject | 有效飯高猜想 | zh_TW |
| dc.subject | Complex threefolds | en |
| dc.subject | Hacon-McKernan conjecture | en |
| dc.subject | effective Iitaka conjecture | en |
| dc.subject | pluricanonical systems | en |
| dc.subject | Betti numbers | en |
| dc.subject | minimal model program | en |
| dc.title | 三維代數多樣體 | zh_TW |
| dc.title | Geometry of Algebraic Threefolds | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 106-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 莊武諺,陳俊成,章源慶,賴青瑞 | |
| dc.subject.keyword | 複三體,極小模型計劃,貝堤數,複正則系統,有效飯高猜想,黑肯-瑪柯能猜想, | zh_TW |
| dc.subject.keyword | Complex threefolds,minimal model program,Betti numbers,pluricanonical systems,effective Iitaka conjecture,Hacon-McKernan conjecture, | en |
| dc.relation.page | 81 | |
| dc.identifier.doi | 10.6342/NTU201801712 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2018-07-19 | |
| 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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