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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 王金龍 | |
| dc.contributor.author | Sz-Sheng Wang | en |
| dc.contributor.author | 王賜聖 | zh_TW |
| dc.date.accessioned | 2021-05-14T17:42:20Z | - |
| dc.date.available | 2015-08-20 | |
| dc.date.available | 2021-05-14T17:42:20Z | - |
| dc.date.copyright | 2015-08-20 | |
| dc.date.issued | 2015 | |
| dc.date.submitted | 2015-08-18 | |
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| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/4450 | - |
| dc.description.abstract | 本文探討在雙有理映射及形變理論的操作下，給出判別三維卡拉比-丘簇的奇異點是否為節點（即米爾諾數等於一）的條件。同時也對於P.S. Green和T. Hübsch教授的結果：在乘積射影空間裡的三維完全交集卡拉比—丘流形皆可由錐過渡變換連接，提供一個詳細的證明。 | zh_TW |
| dc.description.abstract | We develop criteria for a Calabi--Yau 3-fold to be a conifold, i.e. to admit only ODPs as singularities, in the context of extremal transitions. There are birational contraction and smoothing involved in the process, and we give such a criterion in each aspect.
More precisely, given a small projective resolution pi : widehat{X} rightarrow X of Calabi--Yau 3-fold X, we show that (1) If the fiber over a singular point P in X is irreducible then P is a cA_1 singular point, and an ODP if and only if there is a normal surface which is smooth in a neighborhood of the fiber. (2) If the natural closed immersion Def(widehat{X}) hookrightarrow Def(X) is an isomorphism then X has only ODPs as singularities. There are topological constraints associated to a smoothing widetilde{X} of X. It is well known that $e(widehat{X}) - e(widetilde{X}) = 2 | Sing(X) | if and only if X is a conifold. Based on this and a Bertini-type theorem for degeneracy loci of vector bundle morphisms, we supply a detailed proof of the result by P.S.~Green and T.~Hübsch that all complete intersection Calabi--Yau 3-folds in product of projective spaces are connected through projective conifold transitions (known as the standard web). | en |
| dc.description.provenance | Made available in DSpace on 2021-05-14T17:42:20Z (GMT). No. of bitstreams: 1 ntu-104-D98221004-1.pdf: 861956 bytes, checksum: d5fd9acec6286093fe6e54031fd52f38 (MD5) Previous issue date: 2015 | en |
| dc.description.tableofcontents | 口試委員會審定書 . . . . . . . . . . . . . . . . . . . . . .I
中文摘要. . . . . . . . . . . . . . . . . . . . . . . . . .II Abstract. . . . . . . . . . . . . . . . . . . . . . . . . III Acknowledgements. . . . . . . . . . . . . . . . . . . . . IV 1 Introduction 2 2 Preliminaries 8 2.1 Singularities . . . . . . . . . . . . . . . . . . . . . . 8 2.2 Small Birational Morphisms . . . . . . . . . . . . . . 11 2.3 Normal Gorenstein Surfaces . . . . . . . . . . . . . 17 2.4 Augmented Base Locus . . . . . . . . . . . . . . . . .22 2.5 Bertini-type theorems . . . . . . . . . . . . . . . . 23 2.6 Mixed Hodge Structures on Varieties with Normal Crossings 25 3 Deformation Theory of Calabi–Yau threefolds 30 3.1 Unobstructedness Theorem . . . . . . . . . . . . . . .30 3.2 Smoothings . . . . . . . . . . . . . . . . . . . . . .31 4 Decompositions of Small Transitions 33 4.1 Criteria for small reduced fibers . . . . . . . . . . 33 4.2 Decomposition Process of Small Transition . . . . . . 37 5 A Connectedness Theorem of Moduli spaces 42 5.1 Configurations and Parameter Spaces . . . . . . . . . 42 5.2 Determinantal Contractions . . . . . . . . . . . . . .51 5.3 Connecting the CICY Web . . . . . . . . . . . . . . . 54 | |
| dc.language.iso | en | |
| dc.subject | 錐過渡變換 | zh_TW |
| dc.subject | 卡拉比-丘 | zh_TW |
| dc.subject | small contraction | en |
| dc.subject | standard web | en |
| dc.subject | determinantal contraction | en |
| dc.subject | conifold transition | en |
| dc.subject | Calabi-Yau threefold | en |
| dc.title | 三維卡拉比-丘空間奇異點及模空間連結性研究 | zh_TW |
| dc.title | The Connectedness Problem of Calabi--Yau Moduli Spaces | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 103-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 林惠雯,余正道,齊震宇,莊武諺 | |
| dc.subject.keyword | 卡拉比-丘,錐過渡變換, | zh_TW |
| dc.subject.keyword | Calabi-Yau threefold,conifold transition,small contraction,determinantal contraction,standard web, | en |
| dc.relation.page | 62 | |
| dc.rights.note | 同意授權(全球公開) | |
| dc.date.accepted | 2015-08-18 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| 顯示於系所單位： | 數學系 | |
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