Here’s an index of all of the AG from the Beginning articles. I reordered a little bit for coherent topics, and don’t THINK that I screwed up any dependencies (ie, anything should be understood in terms of things higher up on the page than it), but if I did, let me know and I’ll fix it.

Basic Set Up

- Affine Varieties
- Projective Varieties
- Some Commutative Algebra and a bit of Geometry
- Morphisms of Varieties
- Algebraic Groups
- Varieties over other Fields

Projective Geometry

- Gradings on Rings and Modules
- Hilbert Polynomials
- Bezout’s Theorem
- Elliptic Curves
- Veronese Embedding
- Segre Embedding
- Grassmannians and Flag Varieties

Intrinsic Geometry

- Tangent Spaces and Singular Points
- Localization
- Nakayama’s Lemma
- Sheaves
- Morphisms of Sheaves
- Locally Ringed Spaces
- Abstract Varieties
- Complete Varieties and Chow’s Lemma

Computational Geometry

- Groebner Bases and Buchberger’s Algorithm
- Elimination and Extension Theorems
- Resultants
- Computing Hilbert Functions
- Projective Elimination Theory

Relative Geometry

- Sheaves of Modules
- Locally Free Sheaves and Vector Bundles
- Line Bundles and the Picard Group
- Differential Forms and the Canonical Bundle

Linear Systems

Abstract Algebraic Geometry

Cohomology

Curves

- Riemann-Roch Theorem for Curves
- Hurwitz’s Theorem
- Hurwitz’s Theorem on Automorphisms
- Dual Curves
- Plücker Formulas
- Canonical Linear Systems
- Geometric Form of Riemann-Roch
- Constructing Nodal Curves

Schubert Calculus

- Grassmannians Redux
- Schubert Varieties
- Schubert Classes and Cellular Cohomology
- Pieri and Giambelli Formulas
- Applications of the Schubert Calculus

Resolution of Singularities

Hilbert Schemes

- Flat Modules and Morphisms
- Representability of Functors
- Moduli Spaces and Base Change
- The Hilbert Scheme
- Constructing the Hilbert Scheme II
- Flattening Stratifications
- Examples of Moduli Spaces

Matt’s Series on Group Schemes and Moduli

- Group Schemes and Moduli I
- Group Schemes and Moduli II
- Group Schemes and Moduli III
- Group Schemes and Moduli IV

Matt’s Post on Rational Varieties

Matt’s Series on Grothendieck-Riemann-Roch

- Proper Maps and (Quasi) Projective Varieties
- Direct Image Sheaves under Proper Maps
- The Grothendieck Group of Coherent Sheaves on a Variety
- The Grothendieck-Riemann-Roch Theorem, stated
- The Grothendieck-Riemann-Roch Theorem, a proof-sketch

The Hilbert Polynomial Explained

Thanks a lot, this is exactly what I asked for :-)

Now I’m happy, learning your stuff.

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This is rather nice and useful. Well done!

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