Instructor: Martin Olsson
Lectures: MWF 1-2 pm, Room 31 Evans.
Course Control Number: 54542.
Office: 879 Evans
Office Hours: TBA.
Prerequisites: Math 256A or equivalent familiarity with schemes.
Recommended Texts:
Hartshorne, Algebraic Geometry, Springer Graduate Texts in Mathematics 52.
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.
Syllabus: This is the second semester of a year-long 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. I will start this term by discussing differentials, and then cover some curve theory as in Hartshorne's chapter IV. Then I will discuss cohomology. If time permits, I will cover some surface theory at the end of the term
Grading: Grades will be based on weekly homeworks and a term paper.
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.
Course Notes: Notes from the lectures (by James McIvor) can be found here Notes.
Electronic Homework Discussion: Students are asked to upload and discuss their homework solutions using the forum in bspace. If you are not a registered student but attending the course and would like access to this discussion, please send me an email.
Reading period: For those of you making plans for the end of the semester, I will give three lectures during the reading period. Attendance at these lectures is optional. If there is a particular topic you would like me to discuss please let me know.
Problem Set 1: From Vakil (Jan 14, 2012 version): 23.2.F, 23.2.I, 23.2.J, 23.2.K, 23.2.M. Due Friday Jan 27.
Problem Set 2: From Hartshorne. Chapter II, exercises 8.3, 8.4. Chapter IV execises 1.1, 1.2, 1.3, and 1.4 (using Riemann-Roch as a black box). Due Friday Feb 10.
Here is the Black Box.
Problem Set 3: From Hartshorne, Chapter IV. exercises 1.6, 3.1, 3.6, 4.1, 4.4. Due Friday Feb 24.
Problem Set 4: Do problems for Piotr's lectures available here. Due Friday March 9.
Problem Set 5: Hartshorne Chapter II, exercise 1.11. Chapter III, exercises 2.2, 2.3, 2.6, 2.7. Due March 23
Term paper basics are here. This website contains a lot of useful information about mathematical writing.
Problem Set 6: Hartshorne Chapter III, exercises 4.2, 4.5, 4.6, 4.7. Due Friday April 13.