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http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/47268Full metadata record
| ???org.dspace.app.webui.jsptag.ItemTag.dcfield??? | Value | Language |
|---|---|---|
| dc.contributor.advisor | 陳榮凱 | |
| dc.contributor.author | Tian-Shun Feng | en |
| dc.contributor.author | 馮添順 | zh_TW |
| dc.date.accessioned | 2021-06-15T05:52:58Z | - |
| dc.date.available | 2011-08-20 | |
| dc.date.copyright | 2010-08-20 | |
| dc.date.issued | 2010 | |
| dc.date.submitted | 2010-08-18 | |
| dc.identifier.citation | [1] D. Abramovich, K. Matsuki and S. Rashid, A note on the factorization theo-
rem of toric birational maps after Morelli and its toroidal extension, Tohoku Math. J. (2) 51 (1999), no. 4, 489–537. [2] D. Abramovich, K. Karu, K. Matsuki, J. WAlodarczyk, Torification and fac- torization of biratinoal maps, math.AG/9904135 [3] C. Birkar, P .Cascini, C. Hacon, and J. McKernan, Existence of minimal models for varieties of log general type, math.AG/0808.1929 [4] V. Danilov, The geometry of toric varieties, Uspekhi Math. Nauk33 :2(1978), 85-134 = Russian Math Surveys 33:2(1978), 97-154. [5] V. Danilov, Birational geometry of toric 3-folds, Math. USSR Izvestiya Vol.21 (1983), No.2. [6] W. Fulton, Introduction to toric varieties, Annals of Mathematics Studies 131, Princeton University Press, 1993. [7] O. Fujino, and H. Sato, Introduction to the toric Mori theory, math.AG/0307180v2 [8] R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics, No. 52. Springer-Verlag, New York-Heidelberg, 1977 [9] H. Hironaka, On the theory of birational blowing-up, Harvard University Ph.D. Thesis 1960. [10] H. Hironaka, Resolution of singularities of an algebraic variety over a field of characteristic zero, Ann. of Math. 79 1964. [11] H. Hironaka, Flatterning theorem in complex analytic geometry, Amer.J.Math.97, 1975, 503-547. [12] H. Hironaka, An example of a non-K‥alerian complex-analytic deformation of K‥ahlerian complex structure, Annals of Math. (2), 75, 1962, p. 190-208. [13] G. Kempf, F. Knudsen, D. Mumford and B. Saint-Donat, Toroidal embeddings I, 339, Lecture Notes in Mathematics, Springer, 1973. [14] J. Kollar, and S. Mori, Birational geometry of algebraic varieties, Cambreidge Tracts in Mathematics, Vol. 134, 1998. [15] D. Luna, Slices ’etales. Sur les groupes algebriques, pp. 81–105. Bull. Soc. Math. France, Paris, Memoire 33. Soc. Math. France, Paris, 1973. [16] K, Matsuki, Introduction to the Mori program, Universitext, Springer-Verlag, New York, 2002. [17] K, Matsuki, Lectures on factorization of birational maps math.AG/0002084 [18] K, Matsuki, Correction: a note on the factorization theorem of toric birational maps after Morelli and its toroidal extension Tohoku Math. J. 52(2000), 629- 631. [19] R. Morelli, The birational geometry of toric varieties, J. Alg. Geom. 5 1996, 751-782. [20] R. Morelli, Correction to “The birational geometry of toric varieties” , 1997 [21] T. Oda, Torus embeddings and applications , Beased on joint work with Kat- suya Miyake. Tate Inst. Fund. Res., Bombay, 1978. [22] T. Oda, Convex bodies and algebraic geometry, An introduction to the theory of toric varieties, Translated from the Japanese, Ergebnisse der Mathematik und ihrer Grenzgebiete (3) [Results in Mathematics and Related Areas (3)] 15, Springer-Verlag, Berlin, 1988. [23] M. Reid, Decomposition of toric morphisms, Arithmetic and Geometry (Sha- farevich ) volume II, Progress in Math., vol36, Birhauser, 1983, 395-418 [24] J. Sally, Regular overrings of regular local rings , Trans. Amer. math. Soc. 171, 1972, p. 291-300. [25] D. L. Shannon, onoidal transforms, Amer. J. Math. 1973, 45, p. 284-320. [26] J. WAlodarczyk, Toroidal varieties and the weak factorization theorem, Invent. Math. 154(2003), no. 2, 223-331. [27] J. WAlodarczyk, Decomposition of birational toric maps in blow-ups and blow- downs. A proof of the Weak Oda Conjectures, Transactions of the AMS 349, 1997,373-411. [28] J. WAlodarczyk, Simple constructive weak factorization, math.AG/0601649 [29] J. WAlodarczyk,Birational cobordisms and factorization of birational maps, J.Alg. Geom. 9, 2000, 425-449 [30] J. Wisniewski, Toric Mori theory and fano manifolds, Seminaire et Congres 6(2002), 248-272. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/47268 | - |
| dc.description.abstract | 環多樣體是代數幾何中一門特別的旁支, 其最大特點是可用組合方法去研究環多樣體上的幾何. 許多傳統代數幾何中的定理, 在環多樣體中皆有更好與更簡潔的證明, 同時我們亦可將環多樣體當作定理的測試場所, 如1980年代發展起且在近年有重大成就的極小模型理論, Reid 在1982年即在環多樣體上重建了整套極小模型所需的結果.
另一方面 Morelli, WAlodarczyk 於1990年代證明的弱小田定理 (於環多樣體上的弱分解定理) 後不過數年, WAlodarczyk 即推廣此方法至一般的多樣體上, 而其中關鍵是 Morelli 與 WAlodarczyk 在證明弱小田定理時所發展出來的π-奇點消異引理. 本篇論文即是整理此兩樣工作. | zh_TW |
| dc.description.abstract | In this survey, we shall provide basic terminologies, techniques and
applications of toric varieties in algebraic geometry. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T05:52:58Z (GMT). No. of bitstreams: 1 ntu-99-R97221049-1.pdf: 416480 bytes, checksum: 1001bca9cdab67c9ee2df147b86b2185 (MD5) Previous issue date: 2010 | en |
| dc.description.tableofcontents | Contents
Abstract(inChinese) i Abstract(inEnglish) ii Contents iii 1.Introduction 1 2.Preliminaries 5 2.1.Languageoftoricvariety 5 2.2.Singularitiesofpairs 9 2.3.BasicsofGITtheory 10 3.MMPforToricVariety 12 3.1.Contractiontheorem 12 3.2.Existenceofflips 15 3.3.Decompositionoftoricmorphism 17 4.WeakFactorizationofToricBirationalMaps 21 4.1.Reductiontoprojectivemorphismcase 21 4.2.Smoothbirationalcobordism 22 4.3.Morelli’s π-desingularizationlemma 27 4.4.WeakToricFactorization 31 4.5.Proofofthe π-desingularizationlemma 33 References 39 | |
| dc.language.iso | en | |
| dc.subject | 環多樣上的極小模型 | zh_TW |
| dc.subject | 體弱小田定理 | zh_TW |
| dc.subject | 環多樣體 | zh_TW |
| dc.subject | toric MMP | en |
| dc.subject | toric variety | en |
| dc.subject | weak Oda theorem | en |
| dc.title | 環多樣體與其應用 | zh_TW |
| dc.title | Introduction to toric varieties and its applications | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 98-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 王金龍,林惠雯,陳俊成 | |
| dc.subject.keyword | 環多樣體,環多樣上的極小模型,體弱小田定理, | zh_TW |
| dc.subject.keyword | toric variety,toric MMP,weak Oda theorem, | en |
| dc.relation.page | 40 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2010-08-18 | |
| dc.contributor.author-college | 理學院 | zh_TW |
| dc.contributor.author-dept | 數學研究所 | zh_TW |
| Appears in Collections: | 數學系 | |
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| File | Size | Format | |
|---|---|---|---|
| ntu-99-1.pdf Restricted Access | 406.72 kB | Adobe PDF |
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