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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳榮凱 | zh_TW |
| dc.contributor.advisor | Jung-Kai Chen | en |
| dc.contributor.author | 陳毅鴻 | zh_TW |
| dc.contributor.author | Yi-Hung Chen | en |
| dc.date.accessioned | 2024-07-02T16:21:20Z | - |
| dc.date.available | 2024-07-03 | - |
| dc.date.copyright | 2024-07-02 | - |
| dc.date.issued | 2024 | - |
| dc.date.submitted | 2024-06-27 | - |
| dc.identifier.citation | [1] L. Braun. The local fundamental group of a kawamata log terminal singularity. Invet. Math., 226, 2020.
[2] L. Braun, S. Filipazzi, J. Moraga, and R. Svaldi. The jordan property for local fundamental groups. Geometry and Topology, 26:283 – 319, 2022. [3] J. Chen. Explicit resolution of three dimensional terminal singularities. Adv. Stud. Pure Math., 70:323 – 360, 10 2016. [4] D. A. Cox., J. B. Little, and H. K. Schenck. Toric Varieties. Graduate studies in mathematics. American Mathematical Soc., 2011. [5] S. Cutkosky. Elementary contractions of Gorenstein threefolds. Mathematische Annalen, 280(3):521–526, 1988. [6] A. Dimca. Singularities and Topology of Hypersurfaces. 08 2014. [7] A. H. Durfee. Neighborhoods of algebraic sets. Transactions of the American Mathematical Society, 276:517 – 530, 1983. [8] W. Fulton. Intersection theory. Springer New York, second edition, 1998. [9] R. Gurjar and D.-Q. Zhang. π1 of smooth points of a log del pezzo surface is finite: I. J. Math. Sci. Univ. Tokyo, 1, 01 1994. [10] A. Hatcher. Algebraic Topology. Cambridge University Press, 2002. [11] T. Hayakawa. Blowing ups of 3-dimensional terminal singularities. Publications of the Research Institute for Mathematical Sciences, 35:423 – 456, 1999. [12] T. Hayakawa. Blowing ups of 3-dimensional terminal singularities, II. Publications of the Research Institute for Mathematical Sciences, 36:515 – 570, 11 2000. [13] T. Hayakawa. Divisorial contractions to cDV points. PhD thesis, Kanazawa University, 2017. [14] M. Kapovich and J. Kollár. Fundamental groups of links of isolated singularities. Journal of the American Mathematical Society, 27, 09 2011. [15] M. Kawakita. Three-fold divisorial contractions to singularities of higher indices. Duke Math. J., 130(1):57–126, 2005. [16] J. Kollár. New examples of terminal and log canonical singularities. arXiv Preprint, 07 2011. [17] J. Moraga. On termination of flips and fundamental groups, 09 2021. [18] D. Mumford. The topology of normal singularities of an algebraic surface and a criterion for simplicity. Publications Mathématiques de l’Inst. Hautes Sci., 9:5–22, 1961. [19] Z. Tian and C. Xu. Finiteness of fundamental groups. Compositio Mathematica, 153(2):257–273, Feb. 2017. | - |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/92865 | - |
| dc.description.abstract | 這篇論文旨在研究三維奇異點的同調群。我們使用相對同調群和長正和序列來計算第一同調群。我們發現，同調群可以通過一些曲線和除子的交點數來計算。我們期望這個方法可以推廣到高維度。 | zh_TW |
| dc.description.abstract | This note aims to investigate the homology groups of threefold singularities using the relative homology groups and long exact sequences to compute the first homology groups. We find that the first homology groups can be computed by the intersection numbers of some curves and divisors. We expect that this method can be applied to higher dimensions. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2024-07-02T16:21:20Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2024-07-02T16:21:20Z (GMT). No. of bitstreams: 0 | en |
| dc.description.tableofcontents | 致謝 iii
摘要v Abstract vii Contents ix Chapter 1 Introduction 1 Chapter 2 Preliminary 5 2.0.1 Singularities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.0.2 Fundamental Groups . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.0.3 Toric Varieties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9 Chapter 3 Surfaces 13 Chapter 4 Threefolds 19 Chapter 5 Discussion 29 References 31 | - |
| dc.language.iso | en | - |
| dc.title | 奇異點的同調群與基本群 | zh_TW |
| dc.title | Homology Groups and Fundamental Groups of Singularities | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 112-2 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 林學庸;賴青瑞;陳俊成 | zh_TW |
| dc.contributor.oralexamcommittee | Hsueh-Yung Lai;Ching-Jui Lai;Jiun-Cheng Chen | en |
| dc.subject.keyword | 奇異點,同調群,基本群,雙有理幾何,代數幾何, | zh_TW |
| dc.subject.keyword | Singularities,Homology Groups,Fundamental Groups,Birational Geometry,Algebraic Geometry, | en |
| dc.relation.page | 32 | - |
| dc.identifier.doi | 10.6342/NTU202401353 | - |
| dc.rights.note | 同意授權(限校園內公開) | - |
| dc.date.accepted | 2024-06-28 | - |
| 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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