Math 465 Lecture Notes

Caveat lector: These lecture notes are rough and preliminary in form. Please inform me of any errors you might find.

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:

Closed subsets of affine space, Regular functions, and Quasi-projective varieties

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