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| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| 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.
[Bea78] A, Beauville, Complex algebraic surfaces, Astérisque, no. 54, 1978. [BCHM10] C. Birkar, P. Cascini, C. Hacon, J. M c Kernan, Existence of minimal models for varieties of log general type, J. Amer. Math. Soc. 23 (2010), 405-468. [BZ16] C. Birkar, D-Q Zhang, Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs, Publ. Math. de l’IHÉS, 123 (2016), Issue 1, 283-331. [BL04] C. Birkenhake, H. Lange, Complex ablian varieties, Springer-Verlag Berlin Heidelberg (2004). [Bom70] E. Bombieri, The pluricanonical map of a complex surface, Several Complex Variables, I (Proc. Conf., Univ. of Maryland, College Park, Md., 1970), Springer Berlin 1970, 35 – 87. [CT17] P. Cascini, L. Tasin, On the Chern Numbers of a Smooth Threefold, arXiv:1412.1686, to appear in Trans. Amer. Math. Soc.. [CZ14] P. Cascini and D-Q Zhang, Effective Finite Generation for Adjoint Rings, Ann. de l’institut Fourier 64.1 (2014), 127-144. [Che11] J. A. Chen, Explicit resolution of three dimensional terminal singularities, A.S.P.M. (2011), 323-360. [CH09] J. A. Chen, C. Hacon, On the geography of threefolds of general type, J. Algebra 322 (2009), 2500-2507. [CH11] J. A. Chen and C. D. Hacon, Factoring 3-Fold Flips and Divisorial Contractions to Curves, J. Reine Angew. Math., 657 (2011), 173-197. [CM14] J. A. Chen, M. Chen, Explicit birational geometry of 3-folds and 4-folds of general type, III, Compo. Math. 151 (2014), 1041-1082. [CT00] F. Campana, T Peternell, Complex threefolds with non-trivial holomorphic 2-forms, J. Alg. Geom., 9 (2000), 223-264. [Cut88] S. D. Cutkosky, Elementary Contractions of Gorenstein Threefolds, Math. Ann. 280 (1988), no. 3, 521-525. [Dol12] I. V. Dolgachev, Classical Algebraic Geometry: a modern view, Cambridge University Press (2012). [Elk99] N. D. Elkies, The Klein Quartic in Number Theory, In The Eightfold Way: The Beauty of Klein’s Quartic Curve, ed. Sylvio Levi, M. S. R. I. public. 35 (1999), 51-102. [Fuj03] O. Fujino, Algebraic fiber spaces whose general fibers are of maximal Albanese dimension, J. Nagoya Math. 172 (2003), 111-127. [Fuj05] O. Fujino, Remarks on algebraic fiber spaces, J. Math. Kyoto Univ. 45-4 (2005), 683-699. [FM00] O. Fujino, S. Mori, Canonical bundle formula, J. Diff. Geom. 56 (2000), 167-188. [HM06] C. Hacon, J. M c Kernan, Boundedness of pluricanonical maps of varieties of general type, Invent. Math. 166 (2006), 1-25. [Hay99] T. Hayakawa, Blowing Ups of 3-dimensional Terminal Singularities, Publ. Res. Inst. Math. Sci. 35 (1999), 515-570. [Hay00] T. Hayakawa, Blowing Ups of 3-dimensional Terminal Singularities, II, Publ. Res. Inst. Math. Sci. 36 (2000), 423-456. [Hay05] T. Hayakawa, Divisorial Contractions to 3-dimensional Terminal Singularities with Discrepancy One, J. Math. Soc. Japan 57 (2005), 651-668. [Hay1] T. Hayakawa, Divisorial Contractions to cD points, preprint. [Hay2] T. Hayakawa, Divisorial Contractions to cE points, preprint. [Iit70] S. Iitaka, Deformations of compact complex surfaces, II, J. Math. Soc. Japan 22 (1970), no. 2, 247-261. [Kawak01] M. Kawakita, Divisorial Contractions in Dimension Three which Contract Divisors to Smooth Points, Invent. Math. 145 (2001), 105-119. [Kawak05] M. Kawakita, Three-Fold Divisorial Contractions to Singularities of Higher Indices, Duke Math. J. 130 (2005), 57-126. [Kawak12] M. Kawakita, Supplement to Classification of Three-Fold Divisorial Contractions, Nagoya Math. J. 208 (2012), 67-73. [Kawam85] Y. Kawamata, Minimal models and the Kodaira dimension of algebraic fiber spaces, J. reine angew. Math. 363 (1985), 1-46. [Kawam86] Y. Kawamata,On the plurigenera of minimal algebraic 3-folds with K ≡ 0, Math. Ann. 275 (1986), 539-546. [Kol86] J. Kollár, Higher direct images of dualizing sheaf I, Ann. Math. 123 (1986), 11-42. [Kol89] J. Kollár, Flops, Nagoya Math. J. 113 (1989), 15-36. [Kol92] J. Kollár(ed.), Flips and abundance for algebraic threefolds, Astérisque 211, Soc. Math. de. France (1992). [Kol95] J. Kollár, Shafarevich Maps and Automorphic Forms, Princeton University Press (1995). [KM92] J. Kollár, S. Mori, Classification of three-dimensional flips, J. Amer. Math. Soc. 5 (1992), 533-703. [KM98] J. Kollár, S. Mori, Birational geometry of algebraic varieties, Cambridge University Press 1998. [Kot08] D. Kotschink, Chern Numbers and Diffeomorphism Types of Projective Varieties, J. Topol. 1 (2008), no. 2, 518-526. [Laz04] R. Lazarsfeld, Positivity in Algebraic Geometry I, Classical Setting: Line Bundles and Linear Series, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) 48, Springer, Berlin (2004). [Mil64] J.Milnor, On the Betti Numbers of Real Varieties, Proc. Amer. Math. Soc. 15 (1964), 275-280. [Mor82] S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. Math. 116 (1982), 133-176. [Mor85] S. Mori, On 3-dimensional terminal singularities, Nagoya Math. J. 98 (1985), 43-66. [Mor88] S. Mori, Flip Theorem and the existence of Minimal Model for 3-Folds, J. Amer. Math. Soc. 1 (1988), no. 1, 117-253. [Morsn86] D. Morrison, A remark on Kawamata’s paper “On the plurigenera of minimal algebraic 3-folds with K ≡ 0”, Math. Ann. 275 (1986), 547-553. [Rei83] M. Reid, Minimal model of canonical 3-folds, Adv. Stud. pure Math. 1 (1983), 131-180. [Rei87] M. Reid, Young person’ s guide to canonical singularities, Proc. Symp. pure Math. 46 (1987), 345-414. [Rin07] A. Ringler, On a conjecture of Hacon and McKernan in dimension three, arxiv: 0708.3662v2. [Tak06] S. Takayama, Pluricanonical systems on algebraic varieties of general type, Invent. Math. 165 (2006), 551-587. [Tho07] R. Thom, Sur l’homologie des variétés algébriques réelles, Differential and comb. Topology, Princeton University Press (1965), 255-265 [Tsu07] H. Tsuji, Pluricanonical systems of projective varieties of general type II, Osaka J. Math. 44 (2007), 723-764. [Vie83] E. Viehweg, Weak positivity and the additivity of the Kodaira dimension for certain fiber spaces, A.S.P.M. 1 (1983), 329-353. [VZh09] E. Viehweg, D-Q Zhang, Effective Iitaka fibrations, J. Alg. Geom., 18 (2009), 711-730. [VZ01] E. Viehweg, K. Zuo, On the isotriviality of families of projective manifolds over curves, J. Alg. Geom. 10 (2001) 781-799 [Y] Y. Yamamoto, Divisorial Contractions to cDV Points with Discrepancy > 1, preprint. | |
| 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 |
| Appears in Collections: | 數學系 | |
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