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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/61774完整後設資料紀錄
| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 莊武諺(Wu-Yen Chuang) | |
| dc.contributor.author | You-Hung Hsu | en |
| dc.contributor.author | 許佑鴻 | zh_TW |
| dc.date.accessioned | 2021-06-16T13:12:40Z | - |
| dc.date.available | 2016-08-06 | |
| dc.date.copyright | 2013-08-06 | |
| dc.date.issued | 2013 | |
| dc.date.submitted | 2013-07-30 | |
| dc.identifier.citation | [Arca] Daniele Arcara, Stability conditions on derived categories
http://www.math.utah.edu/ arcara/Bridgeland.pdf [Bay] A. Bayer, Polynomial Bridgeland stability conditions and the large volume limit, Geeom. Topol. Vol. 13, pp.2389-2425,2009. [BMT] A. Bayer, E. Macri, Y. Toda, Bridgeland stability conditions on threefold I: Bogomolov-Gieseker type inequalities, 2012. arXiv:math.AG/1103.5010v2. [BBD] A. Beilinson, J. Bermstein, and P. Deligne, Faisceaux Pervers, Asterisque 100, Soc. Math de Paris(1983). [Bez] Roman Bezrukavnikov, Perverse coherent sheaves(after Deligne), 2000. arXiv:math.AG/0005152. [Bri] T. Bridgeland, Stability conditions on triangulated categorues, Ann. of. math., 100(2) 317-346,2007. [Doug] Michael R. Douglas, Dirichlet branes, homological mirroe symmetry, and stability, 2002. arXiv:math.AG/0207021v2. [MP] A. Maciocia, D. Piyaratne, Fourier-Mukai transforms and Bridgeland stability conditions on abelian threefolds, 2013. arXiv:math.AG/1304.3887v2. [PT] R. Pandharipande and R.P.Thomas, Curve counting via stable pairs in the derived category, Invent. math., 178(2009) 400-447. [Ru] Alexei Rudakov, Stability for an Abelian category, Journal of Algebra 197,231-245(1997). [To] Yukinobu Toda, Limit stable objects in Calabi-Yau threefolds, Duke Math. J. 149(2009), 157-208. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/61774 | - |
| dc.description.abstract | 中文摘要
在這篇文章當中，我首先給出Bridgeland 在2007 年刊登 在 Math. Annals 文章[Bri]的讀書調查報告。Bridgeland 的 文章是受到Douglas 在弦論上D-brane 穩定性條件的工作所啟發的。 接下來，由於Bridgeland 對衍生範疇上穩定性條件的定義在3維以上代數多樣體的衍生範疇相當難找到例子， 於是Bayer 在他的文章[Bay]中把Bridgeland 的穩定性條件做 了一些推廣，定義了多項式穩定性條件。這樣讓他找到高 維度代數多樣體衍生範疇上的多項式穩定性條件。 而Bayer 在他的文章當也給出了DT/PT(Donaldosn-Thomas/ Pandharipande-Thomas)對應，他說這個對應可以理 解成多項式穩定性的一種wallcrossing 現象，但是Bayer 的文章只有給出三維代數多樣體上多項式穩定性的 wallcrossing。 於是我們就想要把他的多項式穩定性推廣 到高維度的情況，在文章最後我們也給出了一些高維度的 多項式穩定性，並且證明在這些多項式穩定性條件下的穩 定物件滿足某些特殊的性質。 | zh_TW |
| dc.description.abstract | In this thesis, we give a survey on the concept of the
Bridgeland's stability conditions on derived categories, inspired by Douglas' work on -stability of D-branes in string theory [Doug]. Later, we concern the polynomial stability conditionsby Bayer, and construct some examples of higher dimensional polynomial stability conditions. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-16T13:12:40Z (GMT). No. of bitstreams: 1 ntu-102-R00221010-1.pdf: 409642 bytes, checksum: 1dfa9b62a5924da34595166e3b7fd540 (MD5) Previous issue date: 2013 | en |
| dc.description.tableofcontents | 謝辭 ii
中文摘要 iii 英文摘要 iv 第一章 Stability conditions 1 1.1 Introduction 1 1.2 Stability conditions on abelian categories 2 1.3 t-structures and slicings 5 1.4 Stabilitiy conditions on triangulated categories 8 1.5 Space of stability conditions 10 1.6 Deformation of stability conditions 14 1.7 Structure of the space of stability conditions 20 第二章 Polynomial stability conditions 22 2.1 Introduction 22 2.2 Polynomial stability conditions 23 2.3 Pervese coherent sheaves 23 2.4 DT/PT-correspondence and wallcrossing 25 2.5 Higher dimensional polynomial stability conditions 27 參考文獻 30 | |
| dc.language.iso | en | |
| dc.subject | 衍生範疇 | zh_TW |
| dc.subject | t-結構 | zh_TW |
| dc.subject | Bridgeland穩定性條件 | zh_TW |
| dc.subject | Donaldson-Thomas/Pandharipande-Thomas對應 | zh_TW |
| dc.subject | 多項式穩定性條件 | zh_TW |
| dc.subject | perverse sheaves | en |
| dc.subject | polynomial stability conditions | en |
| dc.subject | Bridgeland stability conditions | en |
| dc.subject | DT/PT correspondence | en |
| dc.subject | wallcrossing | en |
| dc.subject | derived categories | en |
| dc.subject | t-structure | en |
| dc.title | 衍生範疇上的ㄧ些穩定性條件 | zh_TW |
| dc.title | On some stability conditions on derived categories | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 101-2 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 陳榮凱(Jungkai Alfred Chen),王金龍(Chin-Lung Wang),賴青瑞(Ching-Jui Lai) | |
| dc.subject.keyword | Bridgeland穩定性條件,衍生範疇,t-結構,多項式穩定性條件,Donaldson-Thomas/Pandharipande-Thomas對應, | zh_TW |
| dc.subject.keyword | Bridgeland stability conditions,derived categories,t-structure,perverse sheaves,polynomial stability conditions,DT/PT correspondence,wallcrossing, | en |
| dc.relation.page | 31 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2013-07-30 | |
| 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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