Algebraic Geometry I

Department: 
MATH
Course Number: 
6421
Hours - Lecture: 
3
Hours - Lab: 
0
Hours - Recitation: 
0
Hours - Total Credit: 
3
Typical Scheduling: 
Every odd fall

The study of zero sets of polynomials: algebraic varieties, regular and rational map, and the Zariski topology.

Prerequisites: 

MATH 4107 or equivalent

Course Text: 

No text

Topic Outline: 
  • Basic examples and definitions
  • Zariski topology
  • Regular and rational functions
  • Dimension and degree
  • Hilbert basis theorem
  • Nullstellensatz
  • Smooth and singular points
  • Birational maps
  • Normality
  • Divisors
  • Intersection numbers
  • Hilbert functions and polynomials