Instructor: Eric
Urban, Office 521 Math, urban@math.columbia.edu
Time and Place: TR 9:10 - 10:25 in Math. 622.
Text: "
Algebraic Curves, An introduction to algebraic geometry " by
William Fulton
Prerequisite:
Linear algebra, commutative rings and ideals, fields.
Homework: Homework will be assigned every Tuesday and will be due in class two weeks later on Tuesday. Late homework will not be accepted under any circumstances.
Final Exam: The Final Exam date will be announced later. All students must take the final exam at the time scheduled by the University; no final exams can be given earlier or later.
Grading: The course grade is apportioned as follows: Homework 60% and Final exam 40%.
Help: My office
hours are 10:30 -11:30 on TR or by appointment.
| Week |
Topic | Homework problems and
solutions |
| Jan 15 |
Review on algebraic notions, Affine algebraic sets |
|
| Jan 22 |
Hilbert's basis theorem,
Irreducible algebraic sets |
Homework due Feb 5th |
| Jan 29 |
Hilbert's Nullstellensatz
continued |
|
| Feb 5 |
Affine varieties rational functions, local rings, DVR | Homework due Feb 19th |
| Feb 12 |
Plane curves |
|
| Feb 19 |
Projective varieties |
|
| Feb 26 |
Projective plane curves |
|
| Mar 5 |
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| Mar 19 |
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| Mar 26 |
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| Apr 2 |
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| Apr 9 |
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| Apr 16 |
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| Apr 23 |
Review |
|
| Final Examination |