Background from Computational algebraic geometry: These cover considerably more material than what we'll use. Don't worry if you come across topics that were not addressed in lecture!
Lecture 1: January 12
Lecture notes from Dr. Hyeon's course last term:
Class will not meet January 14
Lecture 2: January 16
Introduction: Interpolation problems
Lecture 3: January 21
Affine varieties and regular functions,
Postscript
or
PDF
N.B. We will talk about the Hilbert Basis Theorem later on, so don't
worry about this now. If you're curious, you can find the statement
and proof in Chapter 2
of
Computational algebraic geometry
Lecture 4: January 23
Zariski topology
Lectures 5 and 6: January 26-28
Localization
Lectures 7, 8, and 9: January 30-February 4
Modules
Lectures 10 and 11: February 6-9
Gröbner bases (Revised 2/11/04)
Lectures 12,13,14,15: February 11-18
Modules, continued (Revised 2/18/04)
Lectures 16,17,18: February 20-27
Projective space (Revised 2/27/04)
Lectures 19,20,21,22,23,24,25: March 8-22
Sheaves
Lectures 26,27,28: March 24-29
Localization of modules and
Coherent sheaves
Lectures 29,30,31,32: March 31-April 7
Cech cohomology
Lectures 32,33,34: April 7-12
Cohomology on affine varieties
Lecture 35,36,37: April 14-19
Cohomology on projective varieties