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課程名稱 |
代數幾何一
ALGEBRAIC GEOMETRY (I)(Ⅰ) |
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開課學期 |
108-1 |
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授課對象 |
理學院 數學系 |
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授課教師 |
王金龍 |
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課號 |
MATH5194 |
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課程識別碼 |
221 U8610 |
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班次 |
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學分 |
4.0 |
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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 |
星期二3,4(10:20~12:10)星期四3,4(10:20~12:10) |
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上課地點 |
天數102天數102 |
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備註 |
總人數上限：40人 |
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Ceiba 課程網頁 |
http://ceiba.ntu.edu.tw/1081MATH5194_AG_1 |
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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 |
Foundation of modern algebraic geometry. This course should provide the solid background toward further study on advanced algebraic geometry as well as arithmetic geometry. |
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課程目標 |
To be able to work on varieties and schemes both in the level of local algebras and in the global aspect using cohomology. The first semester (AG-I) should cover the main results in Hartshorne's textbook Chapter 2 and 3, or equivalently half of the contents in Mumford's Algebraic Geometry II. |
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課程要求 |
In order to take the course, besides the standard math majored courses, the student is required to have a solid experience in commutative algebra in the level of Atiyah--MacDonald or half of Eisenbud's book. Familiarity with algebraic topology in the basic level like fundamental groups and covering spaces, homology and cohomology, and basic homological algebra are also required. Students are strongly encouraged to organize seminars on these topics during the summer before taking the course. |
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預期每週課後學習時數 |
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Office Hours |
每週一 13:00~14:00 |
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指定閱讀 |
Hartshorne: Algebraic Geometry
Mumford: Algebraic Geometry I, II |
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參考書目 |
Eisenbud--Harris: The geometry of Schemes
Griffiths--Harris: Principles of Algebraic Geometry
Grothendieck et al: EGA, SGA
Harris: Algebraic Geometry, a first course
Shafarevich: Basic Algebraic Geometry I, II
Stack Project (on internet) |
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評量方式
(僅供參考) |
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週次 |
日期 |
單元主題 |
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Week 1 |
9/10,9/12 |
1.1-1.2, affine and projective varieties |
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Week 2 |
9/17,9/19 |
1.3-1.4, morphisms and rational maps |
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Week 3 |
9/24,9/26 |
1.5-1.6, non-singular varieties and curves |
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Week 4 |
10/01,10/03 |
1.7, intersections in projective spaces |
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Week 5 |
10/08,10/10 |
Homework session of chapter 1 |
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Week 6 |
10/15,10/17 |
2.1-2.2 sheaves and schemes |
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Week 7 |
10/22,10/24 |
2.3-2.4 properties of schemes and morphisms |
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Week 8 |
10/29,10/31 |
2.4-2.5 valuation criterion, O_X-modules |
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Week 9 |
11/05,11/07 |
2.5 coherent sheaves and Serre's theorems |
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Week 10 |
11/12,11/14 |
11/12 HW session, pm 6:00 midterm exam. 2.6 divisors |
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Week 11 |
11/19,11/21 |
2.6-2.7 projective morphisms |
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Week 12 |
11/26,11/28 |
2.8 differentials (2.9 postponed) |
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Week 13 |
12/03,12/05 |
3.1-3.3 sheaf cohomology, affine case |
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Week 14 |
12/10,12/12 |
3.4-3.5 Cech cohomology, projective case |
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Week 15 |
12/17,12/19 |
3.6-3.7 Ext and Tor, Serre duality |
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Week 16 |
12/24,12/26 |
3.8-3.9 direct image and flat morphisms |
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Week 17 |
12/31,1/02 |
3.9 examples of flat families, homework session |
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