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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳榮凱(Jungkai Alfred Chen) | |
| dc.contributor.author | Chih-Chi Chou | en |
| dc.contributor.author | 周致圻 | zh_TW |
| dc.date.accessioned | 2021-06-08T06:19:27Z | - |
| dc.date.copyright | 2006-11-21 | |
| dc.date.issued | 2006 | |
| dc.date.submitted | 2006-11-09 | |
| dc.identifier.citation | [1] Alastair Craw, An introduction to motivic integration. Strings and Ge-ometry,
203-225, Clay Math. Proc. 3, Amer. Math. Soc., Providence, RI, 2004. [2] V. Batyrev. Non-Archimedean integrals and stringy Euler numbers of log-terminal pairs. J. Eur. Math. Soc. 1, pages 5-33, (1999). [3] V. Batyrev, Stringy Hodge numbers of varieties with Gorenstein canonical singularities, Proc. Taniguchi Symposium 1997, In Integrable Systems and Algebraic Geometry, Kobe/ Kyoto 1997, World Sci. Publ. (1999), 1-32. [4] V. I. Danilov, The Geometry of Toric Variety, Russian Math Surveys 33:2 (1978), 97- 154. [5] V. Danilov and A. Khovanskii. Newton polyhedra and an algorithm for computing Hodge-Deligne numbers. Math. USSR Izvestiya 29, pages 279-298, (1987). [6] J. Denef, F. Loeser Germs of arcs on singular algebraic varieties and motivic integration, Invent. Math. 135 (1999), no. 1, 201–232. [7] W. Fulton, Introduction to toric varieties. Annals of Mathematics Studies, 131. The William H. Roever Lectures in Geometry. Princeton University Press, Princeton, NJ, 1993. [8] M. Kontsevich, Lecture at Orsay (december 7, 1995). [9] J. Koll´ar, Singularities of Pairs, in Algebraic Geometry, Santa Cruz 1995, volume 62 of Proc. Symp. Pure math. Amer. Math. Soc. 1997, 221-286 [10] Y. Kawamata, K. Matsuda and K. Matsuki, Introduction to the Minimal Model Program, Adv. Studies in Pure Math. 10 (1987), 283-360. [11] L. Ein, R. Lazarsfeld, M. Mustat¸ˇa Contact Loci in Arc Spaces. arXiv:math.AG/0303268 2004. [12] K. Matsuki, Introduction to the Mori Program. Springer-Verlag, (2002). [13] M. Mustat¸ˇa, Jet Schemes of Locally Complete Intersection Canonical Singularities, Invent. Math. 145 (2001), no. 3, 397–424 [14] M. Mustat¸ˇa, Singularities of Pairs via Jet schemes, J. Amer. Math. Soc. 15 (2002), 599-615. [15] J. Nash, Arc structure of singularities, Duke Math J., 81 (1995),31-38. [16] M. Reid, The McKay correspondence and the physicists’ Euler number conjecture. Lecture notes given at the University of Utah (Sept.), and MSRI (Nov.), (1992). [17] M. Reid, La Correspondence De McKay, Se ´ minaire Bourbaki, 52. [18] M. Reid, The McKay correspondence and the physicists’ Euler number, Lect. Notes given at Univ. of Utah (1992) and MSRI(1992). [19] Yukari Ito and M. Reid, The McKay Correspondence for finite Subgroups of SL(3,C), arXiv:math.AG/9411010 1996. [20] W. Veys, Arc Spaces, Motivic Integration and Stringy Inverients, arXiv:math.AG/0401374 2004. [21] M. Reid, Young Person’s Guide to Canonical Singularities, Algebraic Geometry,V 46, Bowdoin 1985, Proc. of Symposia in Pure Math. [22] K. Watanabe. Certain invariant subrings are Gorenstein I and II. Osaka Journal 11, pages 1-8 and 379-388, (1974). [23] O. Zariski, P Samuel, Commutative Algebra, Volume 2. Princeton, N.J. Van Nostrand, 1958. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/25575 | - |
| dc.description.abstract | In this report, we discuss the topic of arc space and motivic inte-gration
, including some important properties such as the formula of changing variable. With this formula we review Kontsevich’s theorem which states that the Hodge number of crepant resolution is indepen-dent of resolution. Besides, we also review Mustat¸ˇ a’s work that using the knowledge of arc space and motivic integration to give a differ-ent view toward log canonical threshold. At last, Batyrev’s work of proving McKay correspondence is discussed. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-08T06:19:27Z (GMT). No. of bitstreams: 1 ntu-95-R93221033-1.pdf: 327233 bytes, checksum: 84832fa10b93d67c9e58af4c02a72330 (MD5) Previous issue date: 2006 | en |
| dc.description.tableofcontents | 1 Introduction 3
2 Arc Space and Motivic Intergration 3 2.1 Some Lemmas . . . . . . . . . . . . . . . . . . . . . . . . . . . 3 2.2 Arc Space and Motivic Measure . . . . . . . . . . . . . . . . . 5 2.3 Motivic Integration . . . . . . . . . . . . . . . . . . . . . . . . 10 3 Log Canonical Threshold 17 3.1 Introduction to the Main Theorem . . . . . . . . . . . . . . . 17 3.2 Some Geometry Properties of Arc Space . . . . . . . . . . . . 20 3.3 Proof of Theorem 3.1 . . . . . . . . . . . . . . . . . . . . . . . 22 4 McKay Correspondence 23 4.1 Special Case for Toric Variety . . . . . . . . . . . . . . . . . . 24 4.2 Some Lemmas and Definitions . . . . . . . . . . . . . . . . . . 29 4.2.1 Log Pair (X, X) . . . . . . . . . . . . . . . . . . . . . 29 4.2.2 Orbifold E − function . . . . . . . . . . . . . . . . . . 30 4.3 Batyrev’s proof of McKay correspondece . . . . . . . . . . . . 35 5 References 38 | |
| dc.language.iso | en | |
| dc.title | 弧空間上的積分理論及應用 | zh_TW |
| dc.title | On motivic integration and some of its applications | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 95-1 | |
| dc.description.degree | 碩士 | |
| dc.contributor.oralexamcommittee | 蔡宜洵,王金龍 | |
| dc.subject.keyword | 弧空間, | zh_TW |
| dc.subject.keyword | motivic integration, | en |
| dc.relation.page | 40 | |
| dc.rights.note | 未授權 | |
| dc.date.accepted | 2006-11-10 | |
| 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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