Algebraic geometry notes
Note: These notes are based on talks given in a study group organised by Andrew Potter amongst the Bristol postgraduates between 2007 and 2009. They are assuredly full of errors and misunderstandings, since that's how we learn. In short: if you plan to read these notes to learn something about algebraic geometry then you're going to have a bad time. Try James Milne's notes here instead.
2007–2008
- Introduction (Dan Loughran)
- Affine and Projective Varieties (Andrew Potter)
- Functions on Varieties (Lee Butler)
- Dimension and Divisors (Dan Loughran)
- Local Rings of Varieties (Joe Grant)
- Singularities and Blow-Ups (Mike Harvey)
- Uniformisers and Differentials (Lee Butler)
- Quantum Algebraic Geometry (Jon Allcock)
- Spectra of Rings (Dan Loughran)
- Affine Schemes (Andrew Potter)
- Sheaves (Joe Grant)
- Elliptic Curves (DK Huynh)
- Intersections in Projective Space Part I... (Lee Butler)
- ...and Part II (Lee Butler)
- Elliptic Curves and the Weil Conjectures (Andrew Potter)
- Geometry of Surfaces (Mike Harvey)
- Categories and Stuff (Joe Grant)
- Categories, Schemes, & Sheaves (Joe Grant)
2008–2009
- An Affine Recap (Andrew Potter)
- A Projective Recap (Lee Butler)
- Weil Divisors (Dan Loughran)
- Cartier Divisors (Dan Loughran)
- Toric Varieties (Joe Grant)
- Toric Varieties II: The Revenge of the Fan (Joe Grant)
- Algebraic Groups (Lee Butler)
- Complex Multiplication of Elliptic Curves (Andrew Potter)
- Complex Multiplication of Abelian Varieties (Andrew Potter)
- Rational Maps Between Curves and Surfaces (Dan Loughran)
- Semi-Algebraic Geometry (Lee Butler)
- Semi-Algebraic Geometry, Part II (Lee Butler)
- Sheafification (Joe Grant)
- Sheafification 2: Sheafify This! (Joe Grant)
- Étale Cohomology and the Weil Conjectures (Andrew Potter)
- Line Bundles Parts I and II (Dan Loughran)
- Metrized invertible sheaves (Lee Butler)
