Instructor: Martin Olsson
Lectures: MWF 2-3 pm, Room 81 Evans. ROOM SWITCH: Starting Monday 09/10/07 we will meet in 70 Evans.
Course Control Number: 55030
Office: 887 Evans
Office Hours: T 2:45-3:45 and F 3-4.
Prerequisites: A graduate-level course in abstract algebra.
Required Text: Hartshorne, Algebraic Geometry, Springer Graduate Texts in Mathematics 52.
Recommended Texts: Mumford, The red book of varieties and schemes, Lecture Notes in Math 1358.
Dieudonne and Grothendieck, Elements de Geometrie Algebrique, Publ. IHES 4, 8, 11, 17, 20, 24, 28, 32 (1961-1967).
Vakil, Foundations of Algebraic Geometry, course notes available
here.
Syllabus: This course together with its sequel Math 256B in the spring is an introduction to scheme theory and algebraic geometry in its modern formulation. The one-year course will loosely follow Chapter II-V of Harshorne's Algebraic Geometry book, with some supplemental material from other sources. The first semester I hope to cover the basic language of scheme theory and some curve theory. The second semester will be focused on cohomology and surface theory.
Grading: Grades will be based on weekly homeworks.
Homework: There will be weekly homework. This is a very fast course, and it is important to stay up to speed. For this reason no late homework will be accepted.
The GSI for this course is Shenghao Sun. Please see his webpage for his office hours, hints for some homework problems etc.
Problem Set 1. Due Wed. Sep. 5.
Problem Set 2: Hartshorne, Chapter 2, Section 1, Exercises 1.2, 1.3, 1.6, 1.7, 1.8, 1.14, 1.15, 1.16, 1.19, 1.20, 1.22. Due Wed Sep 12.
Problem Set 3. Due Wed. Sep. 19.
Problem Set 4. Due Wed. Sep. 26.
Problem Set 5: Hartshorne, Chapter II, section 3, exercises 3.1, 3.2, 3.3, 3.4, 3.5, 3.6, 3.7, and 3.10.
Problem Set 6: Hartshorne, Chapter II, section 3, exercises 3.8, 3.12, 3.13, 3.14, 3.16, 3.17.
Problem Set 7: Hartshorne, Chapter II, section 3, exercises 3.9, 3.11, 3.15, 3.18, 3.19, 3.22. due Wed. Oct 17.
Problem Set 8: Hartshorne, Chapter II, section 4, exercises 4.1, 4.2, 4.3, 4.4, 4.5, 4.6, due Wed Oct 24.
Problem Set 9: Hartshorne, Chapter II. Section 4, 4.9 and 4.10. Section 5, 5.1, 5.2, 5.4, 5.5, 5.6. due Wed Oct 31.
Problem Set 10: Hartshorne, Chapter II, Section 5, 5.7, 5.8, 5.11, 5.14, 5.15, 5.16, 5.18. Due Wed Nov 7.
Problem Set 11: Hartshorne, Chapter II, Section 5, 5.17, 5.18 (if you didn't do it last week), Section 6, 6.1, 6.4, 6.5. Due Wed Nov 14.
Problem Set 12: Hartshorne, Chapter II, Section 6, 6.6, 6.7, 6.8, , 6.10, 6.11, 6.12. Due Nov 28 (note: in two weeks).
Problem Set 13: Hartshorne, Chapter Section 7, 7.3, 7.4, 7.7, 7.13, Section 8, 8.3, 8.5, 8.8. Due Friday Dec 7. A bonus problem