The purpose of this seminar is to provide an intuitive introduction to modern algebraic geometry.
Lecturer: 陳榮凱 Jungkai Chen
Venue: CCU
Week 1 (2/20) 03:00PM-05:00PM
Lecture 1: Projective space, projective varieties and elliptic curves (video)
Ref: [1, section 4.1, 4.2, 5.1]
Week 2(2/27) 03:00PM-05:00PM
National holiday
Week 3 (3/6) 03:00PM-05:00PM
Lecture 2: Bezout’s theorem and intersection theory (video)
Ref: [1, section 3.1, 3.2, 3.3, 5.3]
Week 4, 5
NCTS Higher Dimensional Algebraic Geometry
3/13-3/17 mini-courses
3/20-3/24 workshop
Week 6 (3/27) 03:00PM-05:00PM
Lecture 3: Singularities and blowups (video)
Ref: [1, chapter 7]
Week 7 (4/3)
Spring break
Week 8 (4/10) 03:00PM-05:00PM
Midterm week 4/10-4/14
Week 9 (4/17)
TA session (video)
Week 10 (4/24) 03:00PM-05:00PM
Lecture 4: Canonical divisors and Riemann-Roch theorem for curves (video)
Ref: [1, chapter 8]
Week 11 (5/1) 03:00PM-05:00PM
Lecture 5: Riemann-Roch theorem for surfaces (video)
Ref: [2, section V.1]
Week 12 (5/8)
TA session (video)
Week 13 (5/15) 03:00PM-05:00PM
Lecture 6: Projective morphisms (video)
Week 14 (5/22)
(video)
Week 15 (5/29) 03:00PM-05:00PM
Lecture 7: Vanishing theorem and extension theorem (video)
Week 16 (6/5)
Presentation
References:
[1] W. Fulton, Algebraic Curves
[2] R. Hartshorne, Algebraic Geometry
It is recommended to read sections 1.1-1.7 and 2.1-2.5 of [1] by yourselves in advance.