I have a copy of the book "Introduction to Toric varieties" by William Fulton, and over the next few months I'd like to make some progress on it.
As a first goal, I'd like to be able to read just the first 3 chapters, which I list some of the sections so people without the book get an idea of the contents:
- Definitions and Examples: Convex polyhedral cones, Affine toric varieties, Fans and torics varieties
- Singularities and compactness: Local properties of toric varieties, Compactness and properness, Resolution of singularities
- Orbits, topology and line bundles: Orbits, Fundamental groups and Euler Characteristics, Cohomology of line bundles
In the next two months I should have covered most of Atiyah-Macdonalds Commutative algebra book. In parallel I was planning to read Fulton's "Algebraic Curves" book (which can be found online here). I already know some cohomology. My question is, will reading "Algebraic Curves" give me enough background in Algebraic geometry to read the 3 chapters on toric varieties? If so, are there any sections of "Algebraic Curves" I could skip? If not, how much more do I need?