請用此 Handle URI 來引用此文件：
http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/98085完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 林學庸 | zh_TW |
| dc.contributor.advisor | Hseuh-Yung Lin | en |
| dc.contributor.author | 林俊廷 | zh_TW |
| dc.contributor.author | Jun-Ting Lin | en |
| dc.date.accessioned | 2025-07-24T16:08:17Z | - |
| dc.date.available | 2025-07-25 | - |
| dc.date.copyright | 2025-07-24 | - |
| dc.date.issued | 2025 | - |
| dc.date.submitted | 2025-07-22 | - |
| dc.identifier.citation | [AGLV98] V. I. Arnold, V. V. Goryunov, O. V. Lyashko, and V. A. Vasil’ev. Singularity Theory I. Springer, 1 edition, 1998.
[AKMW02] D. Abramovich, K. Karu, K. Matsuki, and J. Włodarczyk. Torification and factorization of birational maps. Journal of the American Mathematical Society, 15(3):531–572, 2002. [AT19] D. Abramovich and M. Temkin. Functorial factorization of birational maps for qe schemes in characteristic 0. Algebra Number Theory, 13(2):379–424, 2019. [Ati58] M. F. Atiyah. On analytic surfaces with double points. Proc. R. Soc. Lond. A, 247:237–244, 1958. [BHPV04] W. P. Barth, K. Hulek, C. A. M. Peters, and A. Ven. Compact Complex Surfaces. Springer, 2 edition, 2004. [CG72] C. H. Clemens and P. A. Griffiths. The intermediate jacobian of the cubic threefold. Annals of Mathematics, 95(2):281–356, 1972. [CLS11] D. A. Cox, J. B. Little, and H. K. Schenck. Toric Varieties. American Mathematical Society, 2011. [Dol82] I. Dolgachev. Weighted projective varieties. In J. B. Carrell, editor, Group Actions and Vector Fields, volume 956 of Lecture Notes in Mathematics, pages 34–71. Springer, 1982. [Ess25] L. Esser. Rational weighted projective hypersurfaces. International Mathematics Research Notices, 2025(1), 2025. [Fis76] G. Fischer. Complex Analytic Geometry. Springer, 1976. [Fri83] R. Friedman. A degenerating family of quintic surfaces with trivial monodromy. Duke Math. J., 50(1):203–214, 1983. [Fri85] R. Friedman. Some remarks on the filling in problem for degenerations. Duke Math. J., 52(3):565–575, 1985. [Fuj90] T. Fujita. Classification Theory of Polarized Varieties. Cambridge University Press, 1990. [Hir64] H. Hironaka. Resolution of singularities of an algebraic variety over a field of characteristic zero: I. Annals of Mathematics, 76(1):109–203, 1964. [Hir75] H. Hironaka. Flattening theorem in complex-analytic geometry. Amer. J. Math., 97:503–547, 1975. [KM98] J. Kollár and S. Mori. Birational Geometry of Algebraic Varieties. Cambridge University Press, 1998. [KLSV18] J. Kollár, R. Laza, G. Saccá, and C. Voisin. Remarks on degenerations of hyper-Kähler manifolds. Annales de l’Institut Fourier, 68(7):2837–2882, 2018. [Kol07] J. Kollár. Lectures on Resolution of Singularities. Princeton University Press, 2007. [Kul77] V. S. Kulikov. Degenerations of K3 surfaces and enriques surfaces. Math. USSR-Izv, 11(5):957–989, 1977. [Liu06] Q. Liu. Algebraic Geometry and Arithmetic Curves. Oxford University Press, 2006. [Mor83] J. W. Morgan. Topological triviality of various analytic families. Duke Math. J., 50(1):215–225, 1983. [Mum08] D. Mumford. Abelian Varieties. Hindustan Book Agency, 2 edition, 2008. [Rei87] M. Reid. Young person’s guide to canonical singularities. In S. J. Bloch, editor, Algebraic Geometry-Bowdoin 1985, Part 1, volume 46 of Proc. Symposia in Pure Math., pages 345–414. American Mathematical Society, 1987. [Vik24] Sasha Viktorova. On the classification of singular cubic threefolds. url=https://arxiv.org/abs/2304.10452, 2024. [Voi90] C. Voisin. Degenerations de lefschetz et variations de structures de Hodge. Journal of Differential Geometry, 31(2):527–534, 1990. [Wan97] C.-L. Wang. On the incompleteness of the Weil–Petersson metric along degenerations of Calabi–Yau manifolds. Mathematical Research Letters, 4:157–171, 1997. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/98085 | - |
| dc.description.abstract | 我們研究射影退化中的「光滑填充」問題，即：當一個代數多樣體具有光滑的一般纖維時，是否能將其替換為具有相同一般纖維的光滑家族。在本文中，我們構造了一個三次三維體退變的反例——此退化的單值群有限，但無法被光滑的射影家族所填充。 | zh_TW |
| dc.description.abstract | We study the ”smooth filling‐in” problem for projective degenerations—when a one-parameter family with smooth general fibers can be replaced by a smooth family which has the same general fibers. In this article, we construct a counterexample—a degeneration of cubic threefolds with single A2 singularity—which has monodromy of finite order but cannot be filled with a smooth projective family. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2025-07-24T16:08:16Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2025-07-24T16:08:17Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | Acknowledgements i
摘要 iii Abstract v Contents vii Chapter 1 Introduction 1 1.1 The Smooth Filling-in Problem 1 1.2 Known Results 1 1.3 Fano Counterexamples 2 Chapter 2 Preliminary 3 2.1 Notations and Conventions 3 2.2 Degenerations over the Unit Disc 3 2.3 Bimeromorphic Transforms 3 2.4 Monodromy around A2 Singularity 4 2.5 Finite Quotients of Affine Varieties 6 2.6 Finite Cyclic Quotients 10 2.7 Weighted Projective Spaces 12 2.8 Weighted Blow-ups 13 Chapter 3 Comparison of Bimeromorphic Regular Degenerations 15 Chapter 4 Resolutions of Finite Base Changes of an A2 Singularity 17 4.1 Toric Charts on V′ 18 4.2 Rationality of Ef 22 4.3 Resolution of V′ 23 Chapter 5 Degenerations of Cubic Threefolds 27 5.1 Rigidity of Cubic Threefolds 27 5.2 Nonsingular Cubic Threefolds are not Ruled 28 5.3 Proof of the Main Theorem 29 References 33 | - |
| dc.language.iso | en | - |
| dc.subject | 退變 | zh_TW |
| dc.subject | 解奇異點 | zh_TW |
| dc.subject | 光滑填充 | zh_TW |
| dc.subject | Resolution of Singularities | en |
| dc.subject | Smooth Filling-in | en |
| dc.subject | Degeneration of Hypersurfaces | en |
| dc.title | 光滑填充問題之探究 | zh_TW |
| dc.title | On the Smooth Filling-in Problem | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 113-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 賴冠文;陳正傑 | zh_TW |
| dc.contributor.oralexamcommittee | Kuan-Wen Lai;Jheng-Jie Chen | en |
| dc.subject.keyword | 光滑填充,退變,解奇異點, | zh_TW |
| dc.subject.keyword | Smooth Filling-in,Degeneration of Hypersurfaces,Resolution of Singularities, | en |
| dc.relation.page | 34 | - |
| dc.identifier.doi | 10.6342/NTU202502125 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2025-07-23 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 數學系 | - |
| dc.date.embargo-lift | 2025-07-25 | - |
| 顯示於系所單位： | 數學系 | |
文件中的檔案：
| 檔案 | 大小 | 格式 | |
|---|---|---|---|
| ntu-113-2.pdf | 606.96 kB | Adobe PDF | 檢視/開啟 |
系統中的文件，除了特別指名其著作權條款之外，均受到著作權保護，並且保留所有的權利。