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課程名稱 |
代數幾何導論
Introduction to Algebraic Geometry |
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開課學期 |
100-2 |
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授課對象 |
理學院 數學研究所 |
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授課教師 |
陳榮凱 |
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課號 |
MATH5101 |
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課程識別碼 |
221 U4580 |
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班次 |
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學分 |
3 |
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全/半年 |
半年 |
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必/選修 |
選修 |
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上課時間 |
星期三2,3,4(9:10~12:10) |
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上課地點 |
天數101 |
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備註 |
總人數上限：30人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1002AG |
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課程簡介影片 |
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核心能力關聯 |
本課程尚未建立核心能力關連 |
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課程大綱
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為確保您我的權利,請尊重智慧財產權及不得非法影印
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課程概述 |
Course Outline:
1. Affine and projective varieties, Hilbert Nullstellensatz.
2. Divisors, sheaves and line bundles.
3. Algebraic curves and Riemann surfaces.
4. Riemann-Roch theorem.
5. Kodaira vanishing theorem and Kodaira embedding theorem.
5. Blowing-ups and birational maps.
6. Castelnuovo’s Theorems
7. Minimal models of surfaces.
8. Surfaces with fibrations.
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課程目標 |
Purpose:
This course is designed for student who re interesting in algebraic geometry. For those students who are interesting in algebraic geometry. It's good to have some familiarity with lower dimensional varieties.
The purpose of this course is to introduce higher dimensional algebraic geometry via algebraic curves and surfaces.
Therefore, we will mainly focus on those materials that can be possibly extended to higher dimensional case.
It's going to be a combination of lectures and seminars.
Some topics will be lectured by the instructor and some topics will be presented by participating students.
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課程要求 |
algebra |
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預期每週課後學習時數 |
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Office Hours |
另約時間 |
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指定閱讀 |
H. Clemens, A Scrapbook of Complex Curve Theory
W. Fultonm Algebraic Curves
A. Beauville, Complex Algebraic Surfaces |
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參考書目 |
R. Hartshorne, Algebraic Geometry
D. Mumford, The Red Book of Varieties and Schemes |
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評量方式
(僅供參考) |
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No. |
項目 |
百分比 |
說明 |
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1. |
Presentation and/or Term paper |
70% |
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2. |
Participation |
30% |
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