高維度終端加權投影空間之研究

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陳湛圖(Chen Chan tu) 查詢紙本館藏

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數學系

論文名稱

高維度終端加權投影空間之研究
(A SURVEY ON CLASSIFYING HIGHER DIMENSIONAL TERMINAL AND CANONICAL WEIGHTED PROJECTIVE SPACE)

相關論文

★ 四維度之加權映射之研究	★ An Effective Bound For Sarkisov Program In dimension 2
★ An application of Bezout′s theorem: the effective minimal intersection number of a plane curve	★ 一般型極小曲面之典範映射之研究
★ A survey on the conjecturally minimal volume of klt ample (resp. Fano) varieties and specific classification of 3-folds canonical thresholds in the open interval (1/3,1/2)

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摘要(中)

這篇論文主要探討如何分類具有終端或經典奇點的加權投影空間。一開始先分
類四面體然後根據四面體的結果來分類最小多胞形和最大多胞形。最後分類所
有的三維 Fano 多胞形。我們之後可以引申出在一般維度的結果並應用在四維帶有經典和終端奇點的 Fano 多胞形。

摘要(英)

In this paper, I would offer a detail explanation of ALEXANDER M. KASPRZYK’s paper toricfano three-folds with terminal singularities and Classifying terminal weighted projective space.

關鍵字(中)

★ 經典奇點

關鍵字(英)

★ Fano
★ canonical
★ terminal

論文目次

1 Introduction. 3
2 Preliminary. 5
3 Classifying the tetrahedra. 14
4 Classifying the tetrahedra : The coordinates of the vertices. 19
5 Classifying the minimal polytopes. 28
6 Classifying all Fano polytopes. 34
7 Terminal and canonical weighted projective space. 36
8 Classifications in dimension four 39

參考文獻

[Kas06a] Alexander M. Kasprzyk, Toric Fano threefolds with terminal singularities, Tohoku Math.
J. (2) 58 (2006), no. 1, 101–121.
[Kas09] Alexander M. Kasprzyk, Bounds on fake weighted projective space, Kodai Math. J. 32 32
(2009), 197–208.
[Kas13] Alexander M. Kasprzyk, Classifying terminal weighted projective space .(arXiv:1304.3029)
[NI05] Benjamin Nill, Gorenstein toric Fano varieties.(https://d-nb.info/976200414/34)
[Cox09] David Cox, John Little, and Hal Schenck, Toric Varieties.
[Cox10] David Cox, John Little, and Hal Schenck, Toric Varieties.
[Hart] Robin Hartshorne, Algebraic Geometry . Toric varieties by Cox 32 (2009), 197–208.
[Sca85] H. E. SCARF, Integral polyhedra in three space. Math. Oper. Res. 10 (1985), 403–438.
[Wip] https://en.wikipedia.org/wiki/Pick%27s_theorem
[Mat02] Kenji Matsuki, Introduction to the Mori program, Universitext, SpringerVerlag, New York,
(2002).
[Ful93] Kenji Matsuki, Introduction to Toric Varieties, Annals of Mathematics Studies 131 (1993).
Princeton University Press.
[YPG] Miles Reid, Young person’s guide to canonical singularities.

指導教授

陳正傑(Chen,Jheng-Jie)

審核日期

2022-1-26

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