18.726 Algebraic Geometry

Welcome to 18.726! This course is the second semester of the introductory graduate algebraic geometry sequence. The course will develop the theory of schemes and sheaf cohomology. We will follow the second and third chapters of Hartshorne very closely.

Prerequisites: The first semester algebraic geometry course 18.725. Some familiarity with algebraic topology and complex or differential manifolds helpful.

Time and Venue: Tuesday-Thursday 9:30- 11:00 am in room 2-146

Lecturer: Izzet Coskun, coskun at math.mit.edu

Office: 2-167

Required text: Robin Hartshorne, Algebraic Geometry, Graduate Texts in Mathematics 52, Springer 1977.

Grading: There will be weekly problem sets. There will not be any midterm or final exams. The grade will be entirely based on the problem sets.


  • Here is Craig's write-up of the claim I made in class that given two affine subschemes of a scheme and a point in their intersection, you can find a basic affine for both containing the point.(pdf)
  • Syllabus (pdf)

    Problem Sets:

  • Problem Set 1: Due Feb 13 (pdf)
  • Problem Set 2: Due Feb 22 (pdf)
  • Problem Set 3: Due Feb 27 (pdf)
  • Problem Set 4: Due Mar 6 (pdf)
  • Problem Set 5: Due Mar 13 (pdf)
  • Problem Set 6: Due Mar 20 (pdf)
  • Problem Set 7: Due Apr 3 (pdf)
  • Problem Set 8: Due Apr 10 (pdf)
  • Problem Set 9: Due Apr 24 (pdf)
  • Problem Set 10: Due May 1 (pdf)
  • Problem Set 11: Due May 8 (pdf)
  • Problem Set 12: Due May 15 (pdf)