特殊超曲面奇異點的解析

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姓名

陳志濱(Chih-Pin Chen) 查詢紙本館藏

畢業系所

數學系

論文名稱

特殊超曲面奇異點的解析
(On crepant resolution of some hypersurface singularities)

相關論文

★ A remark on very-ampleness in Toric geometry	★ Special ample divisors in toric 3-folds
★ 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	★ 對角超曲面上奇異點解析的存在性問題
★ Very ampleness of toric 3-folds

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摘要(中)

在此論文中，我們主要的結果是在任何維度中都可以找到一些特殊型式的超曲面，可以將這些超曲面中的奇異點給完全解開，而且這種解開的方法是最精簡的，換句話說，將奇異點解開後體積會保持不變。雖然論文中的主要定理條件相當多，不過也確實提供了很多特殊超曲面奇異點的解析。

摘要(英)

In this thesis, our main result is, for any n-dimensional space,
we can find a suitable weight for some hypersurface, then after a finite number of weight blow up, we arrive at smooth varieties and we get the crepant resolution of the hypersurfaces. Next, we will study what kind of model
has no crepant resolution of hypersurface.

關鍵字(中)

★ 超曲面奇異點的解析

關鍵字(英)

★ crpant resolution of hypersurface singularities

論文目次

Introduction……………………………………………..1
1. Classical blow-up……………………………………….4
2. Weighted projective spaces…………………………….12
3. Weighted blow-up……………………………………...14
4. Main Theorem……………………………………….…17
References………………………………………………22

參考文獻

1. A. Dimca and S. Dimiev, On analytic coverings of weighted rojective spaces, Bull. London Math. Soc. 17 (1985), 234-238.
2. A. Dimca, Singularities and covering of weighted complete intersections, Journal fur Mathematik Band 366 (1986).
3. W. Fulton, Introduction to Toric Varieties, Princeton University Press (1993).
4. Hartshorne, Algebraic Geometry, GTM 52 (1977).
5. H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero:I, Annals of Mathematics Vol. 79, No. 1 (1964), 109-326.
6. V. Kac and K. Watanabe, Finite linear groups whose ring of invariants is a complete intersection, Bull. AMS 6 (1982), 221-223. MR 83h:14042
7. E. Kunz, Introduction to Commutative Algebra and Algebraic Geometry, Birkhauser Boston (1985).
8. Hui-Wen Lin, On crepant resolution of some hypersurface singularities and a criterion for UFD, Trans. of AMS. Vol. 354, No. 5 (2002) 1861-1868.
9. M. Reid, Young person's guide to canonical singularities, Algebraic Geometry Bowdowin 1985, Proc. Symp. Pure Math. 46 (1987), 345-414. MR 89b:14016
10. L. Robbiano, Factorial and almost factorial schemes in weighted projective spaces, Lectures notes in Math 1092 (1984), 62-84.
11. M. Schlessinger, Rigidity of Quotient Singularities, Invent. Math. 14 (1971), 17-26. MR 45:5428

指導教授

林惠雯(Hui-Wen Lin)

審核日期

2004-6-14

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