Math 552 Algebraic Geometry I, Fall 2017

Welcome to Math 552! This course serves as an introduction to Algebraic Geometry. Algebraic Geometry is a central subject in modern mathematics, with close connections with number theory, combinatorics, representation theory, differential and symplectic geometry. We will study basic properties of projective algebraic varieties such as dimension, degree and singularities. At the same time, we will develop a large body of examples that motivate the study of the subject. Depending on time, we will develop the classical theory of curves and surfaces. This course should be enough preparation for a course on the theory of schemes.

Lecturer: Izzet Coskun, coskunizzet@gmail.com

Office hours: MW 10-11, F 11-12 and by appointment in SEO 423

Venue: Taft Hall 304, 12-12:50

Text book: The three recommended texts for this course are:

Prerequisites: A first year graduate course in algebra: familiarity with commutative rings and modules. We will develop the necessary commutative and homological algebra in the course. Familiarity with differential geometry or topology helpful, but not required. The material covered in MATH 549 Differentiable Manifolds should nicely complement this course.

Homework: There will be weekly homework. The homework is due on Wednesdays at the beginning of class. Late homework will not be accepted. You may (in fact, you are encouaged to) work on problems together; however, the write-up must be your own and should reflect your own understanding of the problem.

Grading: The grade will be entirely based on the homework.

Additional references: The following is a list of references that are more advanced, but you might wish to consult them for more in depth treatments of the subject.

Course Notes Available on the Web: The following course notes are really nice. One is more basic and the other more advanced, but you might wish to refer to them.

Lecture notes: I will occassionally post lecture notes here. They are short transcripts of what I planned to say. I make no claims to completeness or accuracy. They are often typed very quickly.

Course materials:

  • The syllabus (pdf).
  • Homework 1, due Friday September 8 (pdf).
  • Homework 2, due Friday September 15 (pdf).
  • Homework 3, due Friday September 22 (pdf).
  • Homework 4, due Friday September 29 (pdf).
  • Homework 5, due Friday October 6 (pdf).
  • Homework 6, due Friday October 13 (pdf).
  • Homework 7, due Friday October 20 (pdf).
  • Homework 8, due Friday October 27 (pdf).
  • Homework 9, due Friday November 3 (pdf).
  • Homework 10, due Friday November 10 (pdf).
  • Homework 11, due Friday November 17 (pdf).
  • Homework 12, due Friday Dec 1 (pdf).