Math 143 (Elementary Algebraic Geometry)
Course structure
- This course will be held online using bCourses and Zoom.
- Zoom: There is a recurring Zoom meeting for our class, scheduled from 9-10AM MTWTh. The Zoom meeting ID will also be posted on bCourses.
- Lectures: I will be recording lectures. They will be posted on bCourses on Monday and Wednesday nights.
- I suggest that you watch the lectures during the Zoom meeting on Tuesdays and Thursdays. That way, if you have questions about the lecture you can pause and ask me.
You can also ask questions in the chat, either publically or privately. - Office hours: I will be holding virtual office hours on Mondays and Wednesdays from 9-10 (in the Zoom meeting). I am also happy to meet with you by appointment.
- There is a Piazza page for the class. See bCourses for the signup link
Homework and tests
- Homework: Homework will be assigned weekly. Assignments and solutions will be posted below, as well as in BCourses. You should turn in you assignments via bCourses. Assignments may be typed using LaTeX, or handwritten and scanned.
- Exams: There will be two midterms and one final exam. They will be "take-home" (ie. stay at home) format and are open book + open notes. You will have one week to do each test. Information on grading can be found in the syllabus above.
Resources
- Here is our syllabus.
- Our official textbook is ''Elementary Algebraic Geometry" by Hulek.
There is an electronic copy avaliable through the library. - We will also use the book ''Algebraic Curves: An Introduction to Algebraic Geometry'' by Fulton.
You can access this book online here: http://www.math.lsa.umich.edu/~wfulton/CurveBook.pdf
Important dates
- First midterm: Assigned February 16, Due February 22
- Second Midterm: Assigned March 16, Due March 22
- Final Exam: Assigned May 8, Due May 14
Lectures
Posted on bCourses every Monday and Wednesday night. To see the lectures, click on "media gallery".
- 1/19: Lectures 1.1,1.2,1.3,1.4
- 1/21: Lectures 2.1,2.2,2.3
- 1/26: Lectures 3.1,3.2,3.3
- 1/28: Lectures 4.1,4.2,4.3,4.4
- 2/2: Lectures 5.1,5.2,5.3. Readings: [H] Section 1.2, [F] Section 1.6, Section 2.1
- 2/4: Lectures 6.1,6.2,6.3,6.4. Readings: [H] Section 1.2.2, [F] Section 2.2
- 2/9: Lectures 7.1,7.2,7.3. Readings: [H] Sections 1.1.3, 1.1.4
- 2/11: Lectures 8.1,8.2,8.3. Readings: [H] Sections 1.1.2, 1.1.3, 1.1.4
- 2/16: Lectures 9.1. Readings: [H] Sections 2.1, 2.2
- 2/18: Lectures 10.1,10.2. Readings: [H] Sections 2.1, 2.2
- 2/23: Lectures 11.1,11.2,11.3. Readings: [H] Sections 2.2, 1.1.1
- 2/25: Lectures 12.1,12.2,12.3. Readings: [H] Section 2.2
- 3/2: Lectures 13.1,13.2,13.3. Readings: [H] Sections 2.2, 2.3
- 3/4: Lectures 14.1, 14.2. Readings: [H] Sections 2.2, 2.3
- 3/9: Lectures 15.1, 15.2, 15.3. Readings: [H] Sections 2.35
- 3/11: Lectures 16.1, 16.2, 16.3, 16.4. Readings: [H] Section 2.3.6
- 3/16: Lectures 17.1, 17.2, 17.3. Readings: [H] Section 3.1
- 3/18: Lectures 18.1, 18.2. Readings: [H] Section 2.3.1, 2.3.2
- 3/30: Lectures 19.1, 19.2, 19.3. Readings: [H] Section 3.1
- 4/1: Lectures 20.1, 20.2, 20.3. Readings: [H] Section 4.2
- 4/6: Lectures 21.1, 21.2, 21.3. Readings: [H] Section 4.2
- 4/8: Lectures 22.1, 22.2, 22.3. Readings: [H] Section 4.2
- 4/13: Lectures 23.1, 23.2, 23.3. Readings: [H] Section 4.1
- 4/15: Lectures 24.1, 24.2. Readings: [H] Section 4.2
- 4/20: Lectures 25.1, 25.2, 25.3. Readings: [H] Section 4.3
- 4/22: Lectures 26.1, 26.2, 26.3, 26.4. Readings: [H] Section 4.3
- 4/27: Lectures 27.1, 27.2, 27.3. Readings: [H] Section 4.3
Homework ([H]=Hulek, [F]=Fulton)
- Homework 1 (due 1/25): [H] Chapter 0, (1), Chapter 1, (1) (changed!); [F] 1.8, 1.11
- Homework 2 (due 2/1): [H] Chapter 1, (2), (3); [F] 1.19, 1.33b
- Homework 3 (due 2/8): [F] 1.22, 1.38, 1.39, 2.2
- Homework 4 (due 2/15): [H] Chapter 1, (6),(7),(9); [F] 1.44 (note: "ring finite" means "finitely generated algebra")
- Homework 5 (due 3/1): [H] Chapter 2, (2),(3); [F] 4.6, 4.15
- Homework 6 (due 3/8): [H] Chapter 2, (5),(6),(7); [F] 4.24
- Homework 7 (due 3/15): [H] Chapter 2, (8),(10), Chapter 3, (8); [F] 6.39 (only the second part)
- Homework 8 (due 4/5): [H] Chapter 3, (1),(2),(3),(4)
- Homework 9 (due 4/12): [H] Chapter 3, (8)(a) (show that V is smooth). Chapter 4, (4), (5), (14)
- Homework 10 (due 4/19): click here (updated 4/16)
- Homework 11 (due 4/26): [H] Chapter 4, (1), (2), (9)
- Homework 12 (due 5/3): [H] Chapter 4, (3), (8) (on problem 3, assume that the curves C_1 and C_2 intersect in exactly nine distinct points P_1,...,P_9. When following the hint, use Bezout's theorem to show that P_1,...,P_8 satisfy the assumptions of problem 2).
Exams
- Exam 1 (due 2/22). solutions (average: 83%)
- Exam 2 (due 3/22). solutions (average: 81%)
- Final exam (due 5/13)