Mathematics 8254 (Introduction to Algebraic Geometry)



Text: Algebraic Geometry by Robin Hartshorne.

Course content: We are going to cover key parts of Chapters II, III (on the machinery of schemes and sheaf cohomology) and IV (on applications of this machinery to curves).

Lecture date Homework assignment
Week 1
Wednesday
January 18
Read Chapter I
Sections 1 through 6
Friday
January 20
Read Chapter I
Section 7
Week 2
Monday
January 23
Chapter I
Exercise 7.1
Wednesday
January 25
Chapter II
Exercises 1.4, 1.14, 1.15, 1.17
Friday
January 27
Chapter II
Exercises 1.1, 1.2, 1.3, 1.5, 1.6, 1.7, 1.8, 1.19, 1.20
Week 3
Monday
January 30
Chapter II
Exercises 2.1, 2.10, 2.13, 2.18, 2.19
Wednesday
February 1
Chapter II
Exercises 2.2, 2.4, 2.5, 2.6, 2.7, 2.9
Friday
February 3
Chapter II
Exercises 2.12, 2.14, 2.15, 2.16, 2.17
Week 4
Monday
February 6
Chapter II
Read Section 2; finish the assigned exercises
Wednesday
February 8
Chapter II
Exercise 3.6
Friday
February 10
Chapter II
Exercises 3.1, 3.2, 3.3, 3.4, 3.5
Week 5
Monday
February 13
Chapter II
Exercises 3.7, 3.9, 3.10, 3.11, 3.12, 3.15, 3.16, 3.20
Wednesday
February 15
Chapter II
Exercises 4.1, 4.2, 4.3
Friday
February 17
Chapter II
Exercises 4.4, 4.6, 4.9
Week 6
Monday
February 20
Chapter II
Exercises 5.1, 5.3, 5.4, 5.6, 5.7, 5.8
Wednesday
February 22
Chapter II
Exercises 5.9, 5.10
Friday
February 24
Chapter II
Read pp. 116-7
Week 7
Monday
February 27
Chapter II
Read pp. 118-9
Wednesday
February 29
Chapter II
Read pp. 120-1
Friday
March 2
Chapter II
Exercises 5.12, 5.13, 5.14
Week 8
Monday
March 5
Chapter II
Exercises 6.1, 6.2, 6.3
Wednesday
March 7
Chapter II
Read pp. 136-40
Friday
March 5
Chapter II
Exercises 6.5, 6.6, 6.7, 6.8
Week 9
Monday
March 19
Chapter II
Read pp. 153-6
Wednesday
March 21
Chapter II
Read pp. 156-60
Friday
March 23
Chapter II
Exercises 7.1, 7.2, 7.5
Week 10
Monday
March 26
Chapter II
Read pp. 175-7
Wednesday
March 28
Chapter II
Read pp. 181-3
Friday
March 30
Chapter III
Read pp. 202-3
Week 11
Monday
April 2
Chapter III
Read pp. 204-5
Wednesday
April 4
Chapter III
Read pp. 206-7
Friay
April 6
Chapter III
Read pp. 207-8
Week 12
Monday
April 9
Chapter III
Read pp. 208-11
Wednesday
April 11
Chapter III
Exercises 3.1-3.8
Friay
April 13
Chapter III
Read pp. 218-20