Syllabus for Math 137

Syllabus for Math 137: Algebraic Geometry

Instructor

Prof. David Helm
Science Center 514
dhelm@math.harvard.edu
Office Hours: Thurs 12-2

Course Assistant

Cameron Freer, sections to be announced.

Lectures

MWF 12-1, in Science Center 507

Required Text

Harris, Algebraic Geometry: A first course
It's also worth looking at J.S. Milne's algebraic geometry lecture notes, which can be found at http://www.jmilne.org/math/CourseNotes/math631.html
Milne's perspective is a little more advanced than the one I want to take, and his terminology is a little different from ours, but it's still a good reference for some of the material that isn't in Harris. The first eight sections will be the most relevant.

Grading

Grades will be based on problem sets and a take-home final. Collaboration on the problem sets (but NOT the final) is encouraged. The first problem set will be due Friday, Feb 18, in class. Late submissions will be penalized 10% per week late (or part thereof).

Course Content

Algebraic Sets and Varieties
- Affine and projective algebraic sets
- Regular functions and coordinate rings
- The Nullstellensatz
- The Zariski topology
- Quasi-projective varieties
Properties of varieties
- Projective morphisms
- Dimension
- Hilbert Polynomials
- Tangent spaces, smoothness, and singularities
Important examples
- Blowing up
- Grassmannians
- Algebraic groups and group actions
- Fano varieties