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

October 24, 2009 at 7:47 pm

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

Now I’m happy, learning your stuff.

January 28, 2010 at 1:06 pm

[...] Trivialities – a group blog about algebraic geometry, with a huge series about “Algebraic Geometry from the Beginning” – which I recommend for it’s little intuitive text-snippets, where you can pick [...]

July 24, 2010 at 2:20 am

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August 23, 2010 at 3:26 pm

[...] at Rigorous Trivialities, Charles has been working for a few weeks on a series of posts about algebraic geometry “from the beginning”. The expository style seems based on a [...]

November 1, 2010 at 10:47 pm

[...] most of all in the context of a project like this are algebraic geometry (for which, small plug, Charles Siegel’s series looks excellent) or category theory (I’ve just gotten started on Mac Lane’s [...]

November 5, 2010 at 3:51 pm

[...] currently reading Charles Siegel’s series of posts on Algebraic Geometry from the beginning and I highly recommend. It’s some of the clearest, loveliest writing ever, and it’s got [...]

December 22, 2010 at 12:28 pm

[...] There are two good resourses that I can follow: the first one is the CRing Project, which is organizing the materials of Commutative Algebra. The other is the posts witten by Professor Ravi Vakil on the Foundations of Algebraic Geometry. These two are really very helpful for me to follow to learn AG. Another one I want to mention is also a blog AG from the Beginning. [...]

October 25, 2012 at 11:25 pm

This is rather nice and useful. Well done!

August 5, 2013 at 9:08 am

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