四維度之加權映射之研究;Weighted Blowups to Cyclic Quotient Terminal Singularity in Dimension 4

Please use this identifier to cite or link to this item: http://ir.lib.ncu.edu.tw/handle/987654321/69510

Title:	四維度之加權映射之研究;Weighted Blowups to Cyclic Quotient Terminal Singularity in Dimension 4
Authors:	林皓正;Hao_cheng,Lin
Contributors:	數學系
Keywords:	加權映射
Date:	2016-01-27
Issue Date:	2016-03-17 20:47:29 (UTC+8)
Publisher:	國立中央大學
Abstract:	這篇論文先介紹森理論中的極小模型理論，接著會看到川又雄二郎先生所計算的結果，他證明在三維度極小模型理論的某種雙有理映射的唯一性。而對於這樣的結果是否能推廣到高維度？事實上，四維度的情形必須要有所限制才能使得該映射唯一。而我在這邊論文裡的計算將會得到一些反例，證明在高維度的情況下存在無限多種的映射。;In this thesis, we shall introduce the Mori program and minimal model program. Kawamata proved that extremal divisorial contraction X->Y which contracts a divisor to a cyclic quotient terminal singularity is unique for threefold case. However, this result may have trouble in higher dimension. In the end of this thesis, we provide some counterexamples and partial results showing that there may be infinitely many choices of the weighted blowups which contracts a divisor to a cyclic quotient terminal singularity in dimension 4.
Appears in Collections:	[Graduate Institute of Mathematics] Electronic Thesis & Dissertation

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