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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 | 蘇品丞 | zh_TW |
| dc.contributor.author | Phin-Sing Soo | en |
| dc.date.accessioned | 2024-07-17T16:31:38Z | - |
| dc.date.available | 2024-07-18 | - |
| dc.date.copyright | 2024-07-17 | - |
| dc.date.issued | 2024 | - |
| dc.date.submitted | 2024-07-12 | - |
| dc.identifier.citation | [BHPV04] Wolf P. Barth, Klaus Hulek, Chris A. M. Peters, and Antonius Van de Ven, Compact Complex Surfaces, second ed., Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 4, Springer-Verlag, Berlin, 2004.
[BT82] R. Bott and L. W. Tu, Differential Forms in Algebraic Topology, Graduate Texts in Mathematics, vol. 82, Springer-Verlag, New York-Berlin, 1982. [CCJ20] Jungkai A. Chen, Meng Chen, and Chen Jiang, The Noether inequality for algebraic 3-folds, Duke Math. J. 169 (2020), no. 9, 1603–1645, With an appendix by János Kollár. [CH17] Yifan Chen and Yong Hu, On canonically polarized Gorenstein 3-folds satisfying the Noether equality, Math. Res. Lett. 24 (2017), no. 2, 271–297. [Che07] Meng Chen, A sharp lower bound for the canonical volume of 3-folds of general type, Math. Ann. 337 (2007), no. 4, 887–908. [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. [CP23] Stephen Coughlan and Roberto Pignatelli, Simple fibrations in (1, 2)-surfaces, Forum Math. Sigma 11 (2023), Paper No. e43, 29. [Har77] Robin Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, vol. No. 52, Springer-Verlag, New York-Heidelberg, 1977. [Hor75] Eiji Horikawa, On deformations of quintic surfaces, Invent. Math. 31 (1975), no. 1, 43–85. [Hor76] Eiji Horikawa, Algebraic surfaces of general type with small c_2^1. I, Ann. of Math. (2) 104 (1976), no. 2, 357–387. [Kem93] G. R. Kempf, Algebraic Varieties, London Mathematical Society Lecture Note Series, vol. 172, Cambridge University Press, Cambridge, 1993. [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. [KO75] Shoshichi Kobayashi and Takushiro Ochiai, Meromorphic mappings onto compact complex spaces of general type, Invent. Math. 31 (1975), no. 1, 7–16. [Kob92] Masanori Kobayashi, On Noether’s inequality for threefolds, J. Math. Soc. Japan 44 (1992), no. 1, 145–156. [Laz04] Robert Lazarsfeld, Positivity in Algebraic Geometry. I, Ergebnisse der Mathematik und ihrer Grenzgebiete. 3. Folge. A Series of Modern Surveys in Mathematics [Results in Mathematics and Related Areas. 3rd Series. A Series of Modern Surveys in Mathematics], vol. 48, Springer-Verlag, Berlin, 2004, Classical Setting: Line Bundles and Linear Series. [Mor82] Shigefumi Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. (2) 116 (1982), no. 1, 133–176. [Noe75] M. Noether, Zur Theorie des eindeutigen Entsprechens algebraischer Gebilde, Mathematische Annalen 8 (1875), no. 4, 495–533. [Ser06] Edoardo Sernesi, Deformations of Algebraic Schemes, Grundlehren der mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 334, Springer-Verlag, Berlin, 2006. [Vak24] R. Vakil, The Rising Sea: Foundations of Algebraic Geometry, https://math.stanford.edu/~vakil/216blog/FOAGfeb2124public.pdf, 2024, Draft as of February 21, 2024. [Wav68] John J. Wavrik, Deformations of branched coverings of complex manifolds, Amer. J. Math. 90 (1968), 926–960. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/93121 | - |
| dc.description.abstract | 本文具體地構造出數個 (2, 4)-型的三維代數多樣體的例子，並描述它們的極小模型 (minimal model) 與正則模型 (canonical model)；這些代數多樣體落在諾特線 (Noether line) 上。對於每個例子 X，我們也計算了上同調空間 H^1(X, T_X) 的維度；該空間描述了 X 的一階形變。這推廣了堀川穎二 (E. Horikawa) 在曲面 (即二維情形) 上的一部份工作。 | zh_TW |
| dc.description.abstract | We construct explicit examples of algebraic threefolds of general type with invariants (vol(X), p_g(X)) = (2, 4) and describe their minimal and canonical model(s); in particular, such threefolds lie on the Noether line. For each of the examples X, we compute the dimension of H^1(X, T_X), the space of first-order infinitesimal deformations of X; this partially generalizes E. Horikawa’s work on surfaces. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2024-07-17T16:31:38Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2024-07-17T16:31:38Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 口試委員會審定書 i
謝辭 iii 摘要 v Abstract vii Contents ix Introduction 1 Chapter 1 Preliminaries 5 Chapter 2 Examples of Threefolds of Type-(2, 4) 11 2.1 The Constructions 11 2.2 Minimal and Canonical Models 19 2.3 Canonical Images 33 2.4 Summary 37 Chapter 3 Moduli Aspects of Threefolds of Type-(2, 4) 39 3.1 Sizes of Space of Deformations 39 3.2 Euler Characteristics 54 Chapter 4 Discussion and Future Work 61 Appendix A C++ Code for Computing Cohomology on Hirzebruch Surfaces 65 References 69 | - |
| dc.language.iso | en | - |
| dc.subject | 雙有理幾何 | zh_TW |
| dc.subject | 模空間 | zh_TW |
| dc.subject | 一般型代數多樣體 | zh_TW |
| dc.subject | 諾特不等式 | zh_TW |
| dc.subject | 環面多樣體 | zh_TW |
| dc.subject | 歐拉示性數 | zh_TW |
| dc.subject | varieties of general type | en |
| dc.subject | birational geometry | en |
| dc.subject | Euler characteristic | en |
| dc.subject | toric varieties | en |
| dc.subject | Noether inequality | en |
| dc.subject | moduli space | en |
| dc.title | 諾特線上(2,4)-型之三維代數多樣體 | zh_TW |
| dc.title | Threefolds on the Noether Line of Type-(2,4) | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 112-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 賴青瑞;陳俊成;林學庸 | zh_TW |
| dc.contributor.oralexamcommittee | Ching-Jui Lai;Jiun-Cheng Chen;Hsueh-Yung Lin | en |
| dc.subject.keyword | 雙有理幾何,模空間,一般型代數多樣體,諾特不等式,環面多樣體,歐拉示性數, | zh_TW |
| dc.subject.keyword | birational geometry,moduli space,varieties of general type,Noether inequality,toric varieties,Euler characteristic, | en |
| dc.relation.page | 71 | - |
| dc.identifier.doi | 10.6342/NTU202401709 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2024-07-15 | - |
| 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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