SYLLABUS

Mathematics 6170

Algebraic Geometry

This is a rough guide to the topics we will cover.

Week 1
Introduction, algebraic sets, complex algebraic manifolds
Week 2
Continued
Week 3
Review of Algebra
Week 4
Varieties, sheaves, morphisms
Week 5
Continued
Week 6
Dimension
Week 7
Separated and complete spaces
Week 8
Continued
Week 9
Introduction to schemes
Week 10
Fields of definition, closed subschemes, functor of points
Week 11
Proper morphisms and finite morphisms
Week 12
Coherent sheaves, line bundles, vector bundles
Week 13
Flat and etale morphisms
Week 14
Normal varieties, Zariski's main theorem