一般型極小曲面之典範映射之研究

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許仕煒(HSU, SHIH-WEI) 查詢紙本館藏

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一般型極小曲面之典範映射之研究
(A survey on the constructions of canonical maps of minimal surfaces of general type)

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摘要(中)

這篇碩士論文在學習如何使用阿貝爾覆蓋來建構一般類型的最小曲面，即給定一個平滑曲面，利用建築數據來建構阿貝爾覆蓋，並且可以計算它的不變量。此外，我們模仿Nguyen Bin的建構方法，在給定一些限制條件下，我們得到他的結果是唯一的。而為了建構，文中我們介紹了代數幾何、阿貝爾覆蓋所需的背景知識：「Robin Hartshorne撰寫的[Algebraic Geometry]第一到五章以及Rita Pardini撰寫的[Abelian cover of algebraic varieties]第一到四章」

摘要(英)

This thesis is to learn how to use abelian cover to construct a minimal surface of general type: that is, given a smooth surface and then use the building data to construct the abelian cover, and its invariant can be calculated. In addition, we imitate Nguyen Bin′s construction method, given some restructions, we get his result is unique. In order to construct, we introduce the background knowledge required for algebraic geometry and abelian cover([Robin Hartshorne, "Algebraic Geometry"] from chapter 1 to chapter 5,[Rita Pardini, "Abelian cover of algebraic varieties"] from chapter 1 to chapter 4.)

關鍵字(中)

★ 阿貝爾覆蓋
★ 一般類型的最小曲面

關鍵字(英)

★ abelian cover
★ minimal surface of general type

論文目次

Contents
1 Introduction1
2 FundamentalKnowledgeofAlgebraicCurves3
2.1 Varietiesandrationalmaps............... 3
2.2 SheavesandSchemes................... 6
2.3 Divisors.......................... 8
2.4 InvertibleSheaves..................... 8
2.5 LinearsystemsandAmpleInvertibleSheaves...... 11
2.6 Blowingups........................ 14
3 FundamentalKnowledgeofAbelianCover16
3.1 Denitionsandproperties................ 16
3.2 Buildingdata....................... 18
4 Exampleofminimalsurfaceofgeneraltypewithcanon-
ical mapofdegree1621
4.1 Propositionof Z42
? covers . ............... 21
4.2 Construction....................... 22
5 Innitefamiliesofabeliancoversofdegree228
5.1 Propositionof Z32
? covers . ............... 28
5.2 Construction....................... 29

參考文獻

References
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16, Arch.Math.(Basel)113(2019),no.4,385{390.
[4] NguyenBin, Some innitesequencesofcanonicalcoversofdegree2, Adv.
Geom. 21(2021),no.1,143{148.
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292 (1992),113-29

指導教授

陳正傑(JHENG-JIE CHEN)

審核日期

2021-8-23

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