### Varieties: An Introduction

- Curves
- Hilbert's Theorems
- Morphisms
- Irreducibility
- Rational Functions
- Birationality
- Projective Space

### Schemes: First Steps

### Schemes: A Closer Study

- Dimension
- Local Structure
- An Interlude on Curves
- Properties of Schemes: The Standard Yoga
- Separated and Proper Morphisms

### Module Theory

- Coherent Sheaves
- Degree and the Hilbert Polynomial
- Divisors
- Vector Bundles
- Linear Systems
- Maps to Projective Space
- Grassmann Varieties

### Differential Forms

### Cohomology

### Algebraic Curves

### Algebraic Surfaces

### Curves on Surfaces

### Algebraic Cycles

*Note:* The list below merely collects together pointers to
various DVI files that I've written during previous attempts to teach
courses and seminars related to algebriac geometry. Unlike the largely
dummy links in the example, concept, and theorem lists, these links
work; they just don't yet point to anything that qualifies as
hypertext. The plan is to convert this raw material (with additions as
necessary) to hypertext versions, and to add the links from the other
viewpoints into the material. These links will disappear as pieces get
converted for absorption into the list above.

- Basic Tools
- Intersection Theory
- Chern Classes
- Numerical Invariants
- Ampleness and Adjunction
- Castelnuovo's Criterion
- Ruled Surfaces
- Kodaira Dimension Zero
- Abelian and Enriques Surfaces

- Intersections and Cycles: An Introduction
- Algebraic
`K`-theory and Algebraic Cycles - Relative Effective Cartier Divisors
- Linear Systems
- Vanishing Theorems
- The Semicontinuity Theorem
- Universal Families of Curves
- The Picard Scheme
- Good Curves
- The Hodge Index Theorem
- Independent Zero Cycles

Comments on this web site should be addressed to the author:

Kevin R. CoombesDepartment of Biomedical Informatics

The Ohio State University

Columbus, Ohio 43210