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姓名 李忠逵(Chung-Kuei Lee) 查詢紙本館藏 畢業系所 數學系 論文名稱 對角超曲面上奇異點解析的存在性問題
(Existence Problems about Crepant Resolutions of Diagonal Hypersurfaces)相關論文
★ A remark on very-ampleness in Toric geometry ★ Special ample divisors in toric 3-folds ★ 特殊超曲面奇異點的解析 ★ 一個解開環面簇的奇異點的有效方法(一般情形) ★ 一個解開環面簇的奇異點的有效方法(三維情形) ★ 三維 Flip 的存在性之討論 ★ Very ampleness of toric 3-folds 檔案 [Endnote RIS 格式]
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摘要(中) 在這篇文章中，我們使用 weighted blowup 為工具，對一些 C^n+1 中的對角超曲面作出了Crepant Resolution。我們也發現了幾條 n維 variety 沒有 Crepant Reolutions的充分條件。搭配上 Grothendieck 的部份研究結果，我們給出了有效率發現沒有 Crepant Resolution 的對角超曲面的方法。 摘要(英) In this article, we use the weighted blowup to determine some diagonal hypersurfaces in Cn+1 which admit crepant resolutions. We also find some sufficient conditions on n-dimensional varieties such that they have no crepant resolutions. Together with Grothendieck’s result, we provide an effective way to find diagonal hypersurfaces
without crepant resolutions.關鍵字(中) ★ 存在 關鍵字(英) ★ Crepant Resolution 論文目次 中文摘要 …………………………………… i
英文摘要 …………………………………… ii
Contents …………………………………… iii
Abstract …………………………………… 1
1.Introduction …………………………………… 2
2.Weighted Crepant Blowup …………………………………… 5
3.Main Results ……………………………………10
3.1 Existence of Crepant Resolutions ………………………10
3.1.1 Main Theorems ……………………………………10
3.1.2 Analysis of Theorem 3.2. ……………………………13
3.1.3 Systematical Construction of Examples …………… 13
3.2 Non-Existence of Crepant Resolutions ……………… 16
References ………………………………… 18
Appendix A ………………………………… 19
Appendix B ………………………………… 22參考文獻 [Ch] Zhi-Bin Chen, On creapnt resolution of some hypersurface singularities,Master Thesis, Department of Mathematics, NCU, 2004
[Fl] H. Flenner, Divisorenklassengruppen quasihomogener Singularitaten, J. Reine Angew. 328 (1981), 128-160.
[KMM] Y. Kawamata, K. Matsuda, and K. Matsuki, Introduction to the minimal model problem, Algebraic Geometry, Sandai, 1985 (T. Oda, ed.). Adv. Stud. Pure Math. vol 10. North-Holland, Amsterdam, 1987, 283-360.
[Lin] Hui-Wen Lin, On crepant resolution of some hypersurfaces singularities and a criterion for UFD, Trans. of AMS. Vol. 354, No.5 (2002) 1861-1868
[Re1] M. Reid, Young person's guide to canonical singularities, Algebraic Geometry Bowdowin 1985, Proc. Symp. Pure Math. 46 (1987), 345-414.
[Re2] M. Reid, Canonical threefolds, Journ ees de G eom etrie d'Angers 1979, ed. A. Beauville, Sijtho & Noordho , Alphen aan den Rijn, 1980, 273-310.
[Ro] S.-S Roan, Minimal Resoluition of Gorenstein Orbifolds in Dimenision Three, Topology 35 (1996), 489-508
[Rob] L. Robbiano, Factorial and almost factorial schemes in weightedprojective spaces, Lecture notes in Math 1092 (1984), 62-84
[Sc] M. Schlessinger, Rigidity of Quotient Singularities, Invent. Math. bf14 (1971), 17-26.18指導教授 林惠雯(Hui-Wen Lin) 審核日期 2008-6-25 推文 plurk
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