Math 7141: Basic Algebraic Geometry I

This course will be an introduction to the theory of algebraic varieties.  We will develop the basic properties of affine and projective varieties, see some classical constructions, and time permitting, prove the Riemann-Roch theorem for curves.

Classes are on Monday, Wednesday, and Friday, 11:30am - 12:25pm, in Bolz 120.


As a main text, we will use Basic Algebraic Geometry I, 3rd ed., by Igor Shafarevich.  However, I will also draw on other sources, and among them, I strongly recommend that you also read:

These notes from a course by Andreas Gathmann
Algebraic Curves by William Fulton
The Red Book of Varieties and Schemes, by David Mumford

For those interested in continuing with algebraic geometry: A thorough understanding of commutative algebra (say from Atiyah-Macdonald or Matsumura) will be helpful for this first course, but it is absolutely essential for understanding modern algebraic geometry.  A common plan for follow-up study is to learn the basic theory of schemes, following Chapters II and III of Algebraic Geometry by Robin Hartshorne. 


Grades will be based on homework assignments.
HW1: PDF, due 9/8.
HW2: PDF, due 9/17.
HW3: PDF, due 9/29.
HW4: PDF, due 10/13.
HW5: PDF, due 10/22.
HW6: PDF, due 11/3.
HW7: PDF, due 11/22.
HW8: PDF, due 12/8.