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| DC 欄位 | 值 | 語言 |
|---|---|---|
| dc.contributor.advisor | 陳榮凱(Jung-Kai Chen) | |
| dc.contributor.author | Jheng-Jie Chen | en |
| dc.contributor.author | 陳正傑 | zh_TW |
| dc.date.accessioned | 2021-06-15T04:48:28Z | - |
| dc.date.available | 2010-08-05 | |
| dc.date.copyright | 2010-08-05 | |
| dc.date.issued | 2010 | |
| dc.date.submitted | 2010-08-03 | |
| dc.identifier.citation | Bibliography
[1] S. Altinok, G. Brown, M. Reid, Fano 3-folds, K3 Surfaces and graded rings. Topology and geometry: commemorating SISTAG, 25-53, Contemp. Math., 314, Amer.Math. Soc., Providence, RI, 2002. [2] S. Altinok and M. Reid, Three Fano 3-folds with $| − K| $=$ emptyset$, Preprint. [3] G. Brown, K. Suzuki, Fano 3-folds with divisible anticanonical class, Manuscripta Math. 123 (2007), 37–51. [4] A. Corti, A. Pukhlikov, M. Reid, Fano 3-folds hypersurfaces. Explicit birational geometry of 3-folds, 175-258, London Math. Soc. Lecture Note Series, 281. Cambridge University Press, Cambridge, 2000. [5] J. A. Chen, M. Chen, Explicit birational geometry for 3-folds of general type, preprint. arXiv: 0706.2987. [6] J. A. Chen, M. Chen, Explicit birational geometry of 3-folds of general type I, Ann Sci Ecole Norm Sup (to appear). arXiv: 0810.5041. [7] J. A. Chen, M. Chen, Explicit birational geometry of 3-folds of general type II, Journal of Differential Geometry (to appear). arXiv:0810.5044. [8] J. A. Chen, M. Chen, An optimal boundedness on weak $mathbb{Q}$-Fano 3-folds, Adv. Math. 219(2008), 2086-2104. arXiv: 0712.4356. [9] J.J. Chen, J.A. Chen, M. Chen On quasismooth weighted complete intersections, Jour. Alg. Geom, to appear. arXiv 0908.1439. [10] A. Dimca, Singularities and coverings of weighted complete intersections. J. Reine Angew. Math. 366 (1986), 184-193. [11] I. Dolgachev, Weighted projective space, Group actions and vector fields, Proc. Vancouver 1981 LNM 956, 34-71 Springer Verlag. [12] R. Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics 52, Springer-Verlag, New York, Heidelberg, Berlin, 1977. [13] T. Hayakawa, Blowing Ups of 3-dimensional Terminal Singularities, Publ. RIMS. Kyoto Univ., 35 (1999), 515-570. [14] T. Hayakawa, Blowing Ups of 3-dimensional Terminal Singularities II, Publ. RIMS. Kyoto Univ., 36, Number 3 (2000), 423-456. [15] A. R. Iano-Fletcher, Contributions to Riemann-Roch on projective 3-folds with only canonical singularities and applications, Proc. Symposia in Pure Math 46 (1987) Vol 1, pp. 221-231. [16] A. R. Iano-Fletcher, Working with weighted complete intersections, Explicit birational geometry of 3-folds, 101-173, London Math. Soc. Lecture Note Series, 281. Cambridge University Press, Cambridge, 2000. [17] M. Kawakita, Divisorial contractions in dimension three which contract divisors to smooth points, Inventiones Mathematicae 145 (2001), 105-119. [18] Y. Kawamata, Boundedness of $mathbb{Q}$-Fano threefolds. Proceedings of the International Conference on Algebra,Part 3 (Novosibirsk,1989), 439–445, Contemp. Math., 131, Part 3, Amer. Math. Soc., Providence, RI, 1992. [19] Y. Kawamata, Divisorial contractions to 3-dimensional terminal quotient singularities, Higher dimensional complex varieties, de-Gruyter, Berlin. 1996) 241-246. [20] Y. Kawamata, On the plurigenera of minimal algebraic 3-folds with K$equiv $0, Math. Ann. 275 (1986) 539-546. [21] Y. Kawamata, K. Masuda, K. Matsuki, introduction to minimal model problem, Adv. Stud. Pure Math. 10, Alg. Geom., Sendai, T.Oda ed.(1985) , 283-360. [22] V. A. Khinich, When is a ring of invariants of a Gorenstein ring also Gorenstein?, Izv. Akad. Nauk SSSR Ser. Mat. 40 (1976) 50-56=Math. USSR Izv. 10 (1976) 47-54. [23] J. Koll´ar, Shafarevich maps and automorphic forms. M. B. Porter Lectures. Princeton University Press, Princeton, NJ, 1995. [24] J. Koll´ar, S. Mori, Birational geometry of algebraic varieties, M. B. Porter Lectures. Princeton University Press, Princeton, NJ, 1995. [25] J. Koll´ar, S. Mori, Classification of three dimensional flips, J. Amer. Math. Soc., 5 (1992), 533-703. [26] J. Koll´ar, Y. Miyaoka, S. Mori, H. Takagi, Boundedness of canonical $matbb{Q}$-Fano 3-folds, Proc. Japan Acad. 76, Ser. A (2000), 73-77. [27] M. Reid, Minimal models of canonical 3–folds, Advanced studies in Pure Math. 1, Analytic varieties and algebraic varieties, (1983) 131-180. [28] M. Reid, Canonical 3-folds, Journ´ees de G´eom´etrie Alg´ebriqued’Angers, A. Beauville (editor), Sijthoff and Noordhoff, Alphenaan den Rijn, 1980, pp. 273-310. [29] M. Reid, Young person’s guide to canonical singularities, Proc. Symposia in pure Math. 46(1987), 345-414. [30] K. Suzuki, On Fano indices of $mathbb{Q}$-Fano 3-folds, Manuscripta Math. 114 (2004), 229-246. [31] S. Mori, Threefolds whose canonical bundles are not numerically effective, Ann. of Math. 116 (1982), 133-176. [32] S. Mori, On 3-dimensional terminal singularities, Nagoya Math J. 98(1985), 43-66. [33] S. Mori, D. R. Morrison and I. Morrison, On four-dimensional terminal quotient singularities, Math. Comp. 51 (1988), 769–786. [34] K. Watanabe, Certain invariant subrings are Gorenstein,I and II, Osaka J. Math. 11 (1974) 1-8 and 379-388. [35] L. Zhu, The sharp lower bound for the volume of 3-folds of general type with $chi$ $mathcal{O}_X = 1$, Math. Z. 261 (2009), 123-141. arXiv:0710.4409. | |
| dc.identifier.uri | http://tdr.lib.ntu.edu.tw/jspui/handle/123456789/45902 | - |
| dc.description.abstract | We give the codimension bound for quasismooth weighted
complete intersections and also provide several complete lists on quasismooth weighted complete intersections which are terminal 3-folds (cf. [16]) and prove the finiteness of these families for every fixed amplitude . We have two counterexamples (which are different from 3-folds) for higher dimensional varieties with only terminal singularities. We prove the divisorial contraction to terminal cyclic quotient $(X, P) = C^n/Z_r(a_1, a_2, ..., a_n)$ with minimal discrepancy $1/r$ is unique. | en |
| dc.description.provenance | Made available in DSpace on 2021-06-15T04:48:28Z (GMT). No. of bitstreams: 1 ntu-99-D94221006-1.pdf: 623213 bytes, checksum: d5cb0737c4062e0aa428bd4b14065015 (MD5) Previous issue date: 2010 | en |
| dc.description.tableofcontents | Contents
1. Introduction 1 2. Back ground materials 4 3. Proof of theorem 1.3 6 4. Singularities and some theorems 9 5. General properties of w.c.i. threefolds and the classification of weighted terminal Calabi-Yau threefolds 11 6. Examples and finiteness of weighted complete intersections 15 7. Baskets of singularities 18 8. Weighted terminal Q-Fano 3-folds 24 9. Weighted terminal 3-folds of general type 25 10. Weighted terminal 3-folds for several amplitudes $alpha$$leq$ −2 and $alpha$ =2 28 11. Generalization of theorem 1.3 and embedding dimension 31 12. Divisorial contractions to terminal cyclic quotient singularities 34 13. Tables of complete lists 41 Bibliography 49 | |
| dc.language.iso | en | |
| dc.title | 高維度奇異點之研究 | zh_TW |
| dc.title | On Higher Dimensional Singularities | en |
| dc.type | Thesis | |
| dc.date.schoolyear | 98-2 | |
| dc.description.degree | 博士 | |
| dc.contributor.oralexamcommittee | 王金龍(Chin-Lung Wang),林惠雯(Hui-Wen Lin),陳俊成(Jiun-Cheng Chen),夏杼(Zhu Eugene Xia),王立中(Lih-Chung Wang) | |
| dc.subject.keyword | 高維度奇異點,半平滑,加權完全相交的曲體,完備列表,嵌入維度,川又雄二郎blowup,加權blowup, | zh_TW |
| dc.subject.keyword | higher dimensional singularities,quasismooth,weighted complete intersections,complete lists,embedding dimension,Kawamata blowup,weighted blowup, | en |
| dc.relation.page | 51 | |
| dc.rights.note | 有償授權 | |
| dc.date.accepted | 2010-08-04 | |
| 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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