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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 林學庸 | zh_TW |
| dc.contributor.advisor | Hsueh-Yung Lin | en |
| dc.contributor.author | 黃建順 | zh_TW |
| dc.contributor.author | Jian-Shun Huang | en |
| dc.date.accessioned | 2025-02-27T16:28:59Z | - |
| dc.date.available | 2025-02-28 | - |
| dc.date.copyright | 2025-02-27 | - |
| dc.date.issued | 2025 | - |
| dc.date.submitted | 2025-02-12 | - |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/97163 | - |
| dc.description.abstract | 這篇論文的主要目標是研究射影對偶的退化。我們證明在特定條件下，一個 向量叢截面的零點集構成的光滑族的平坦極限可以描述為額外法叢截面的零點 集。作為應用，我們探討 Shinder-Zhang 的五次橢圓曲線，並證明它們會退化為 Mori-Mukai 連結中，三維二次曲面中的一條橢圓曲線。 | zh_TW |
| dc.description.abstract | The primary aim of this note is to initiate the study of the degenerations of projective dualities. We prove that, under certain conditions, the flat limit of a smooth family of zero loci of general sections of a vector bundle can be described as the zero locus of a section of the excess normal bundle. As an application, we examine the case of Shinder-Zhang’s degree-five elliptic curves and show that they degenerate to the elliptic curve on the quadric 3-fold, appearing in the Mori-Mukai link of Fano 3-fold. | en |
| dc.description.provenance | Submitted by admin ntu (admin@lib.ntu.edu.tw) on 2025-02-27T16:28:59Z No. of bitstreams: 0 | en |
| dc.description.provenance | Made available in DSpace on 2025-02-27T16:28:59Z (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 Preliminaries 5 2.1 Algebraic Groups 5 2.2 Homogeneous Varieties 6 2.3 Flat Limit 7 2.4 Zero Locus of a General Section. 9 Chapter 3 Main Result 11 3.1 Setup for the Main Theorem 11 3.2 Main Theorem 12 Chapter 4 Application 17 4.1 Canonical bundle of Gr(k, n) 17 4.2 Shinder-Zhang’s Elliptic Curves of Degree 5 18 4.3 Non-transverse Intersection 19 4.3.1 Isotropic Grassmannian 19 4.3.2 Non-transverse intersection 20 4.4 Calabi-Yau pair of Homogeneous Roof of Type C2 22 4.4.1 Quadric 3-folds and spinor bundles 22 4.4.2 Degeneration 23 References 29 | - |
| dc.language.iso | en | - |
| dc.subject | 齊性多樣體 | zh_TW |
| dc.subject | 相交 | zh_TW |
| dc.subject | 退化 | zh_TW |
| dc.subject | 額外法叢 | zh_TW |
| dc.subject | 代數幾何 | zh_TW |
| dc.subject | Algebraic Geometry | en |
| dc.subject | Degeneration | en |
| dc.subject | Excess Normal Bundle | en |
| dc.subject | Intersection | en |
| dc.subject | Homogeneous Variety | en |
| dc.title | 關於射影對偶的退化 | zh_TW |
| dc.title | On Degenerations of Projective Dualities | en |
| dc.type | Thesis | - |
| dc.date.schoolyear | 113-1 | - |
| dc.description.degree | 碩士 | - |
| dc.contributor.oralexamcommittee | 王賜聖;賴冠文 | zh_TW |
| dc.contributor.oralexamcommittee | Sz-Sheng Wang;Kuan-Wen Lai | en |
| dc.subject.keyword | 退化,額外法叢,相交,齊性多樣體,代數幾何, | zh_TW |
| dc.subject.keyword | Degeneration,Excess Normal Bundle,Intersection,Homogeneous Variety,Algebraic Geometry, | en |
| dc.relation.page | 33 | - |
| dc.identifier.doi | 10.6342/NTU202500514 | - |
| dc.rights.note | 同意授權(全球公開) | - |
| dc.date.accepted | 2025-02-13 | - |
| dc.contributor.author-college | 理學院 | - |
| dc.contributor.author-dept | 數學系 | - |
| dc.date.embargo-lift | 2025-02-28 | - |
| 顯示於系所單位： | 數學系 | |
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