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 - 12:35pm, in MW 154.
As a main text, we will follow these notes from a course by Andreas Gathmann. However, I will also draw on other sources, and among them, I strongly recommend that you also read:
|Algebraic Curves by William Fulton|
|Basic Algebraic Geometry I, 3rd ed., by Igor Shafarevich|
|The Red Book of Varieties and Schemes, by David Mumford|
For those interested in continuing with the second semester: A thorough understanding of commutative algebra (say from Atiyah-Macdonald or Matsumura) will be helpful for the first semester, but absolutely essential for the second semester. The usual plan is to introduce the basic theory of schemes in 7142, 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 9/15.|
|HW3: PDF, due 9/22.|
|HW4: PDF, due 10/6.|
|HW5: PDF, due 10/20.|
|HW6: PDF, due 11/3.|
|HW7: PDF, due 11/17.|
|HW8: PDF, due 12/4.|