Blogs about: Algebraic Geometry From The Beginning
Flat Modules and Morphisms
Charles wrote 3 days ago: Especially after yesterday, today’s going to feel very algebraic. That’s because we … more »
Bertini's Theorem
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Charles wrote 4 days ago: Today we’re going to prove a theorem of Bertini’s. Next time, we’ll focus on usin … more »
Blowing things up
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Charles wrote 1 week ago: In my post on Resolution of Singularities, I talked about three means of resolving singularities of … more »
Normalization and Normal Varieties
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Charles wrote 1 week ago: I got four people that seemed more-or-less to want me to keep going with these, so I have decided to … more »
Riemann-Roch Theorem for Curves
Charles wrote 1 month ago: Today we’re going after one of the most famous theorems of algebraic geometry: the Riemann-Roc … more »
Serre Duality
Charles wrote 1 month ago: Sorry that this one is late, things are going to continue to be hit-or-miss through June, though hop … more »
Cohomology of Sheaves
Charles wrote 1 month ago: In order to get at surfaces, we don’t just need the scheme theory of the last two posts, but w … more »
Proj of a Graded Ring and Basic Properties of Schemes
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Charles wrote 1 month ago: Last time, we talked about , which takes rings and gives us affine schemes in a manner analogous to … more »
Schemes
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Charles wrote 1 month ago: Sorry about the extended delay, should be back to regular Monday-Wednesday-Friday updates now. I ho … more »
Linear Systems
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Charles wrote 3 months ago: Ok, so last time, we discussed divisors. We’re going to keep going in that direction now, and … more »
Weil Divisors, Cartier Divisors and more Line Bundles.
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Charles wrote 3 months ago: Some people might say that the natural place for this topic is before talk of differential forms and … more »
Differential Forms and the Canonical Bundle
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Charles wrote 3 months ago: We’re going to need to start out the day with a bit of algebra, because we’re going to t … more »
Line Bundles and the Picard Group
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Charles wrote 3 months ago: We’ve now talked about vector bundles and locally free sheaves, we’re going to specify t … more »
Locally Free Sheaves and Vector Bundles
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Charles wrote 3 months ago: Last time, we talked about sheaves of modules, and focused on the correspondence between sheaves of … more »
Complete Varieties and Chow's Lemma
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Charles wrote 3 months ago: First off, I’d like to make a correction to the definition of an abstract variety: we’re … more »
Abstract Varieties
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Charles wrote 4 months ago: Last time, we defined locally ringed spaces and I linked back to an old post where I defined the not … more »
Locally Ringed Spaces
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Charles wrote 4 months ago: Sorry about February, got rather caught up in schoolwork. My posts should resume, though still not … more »
Morphisms of Sheaves
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Charles wrote 5 months ago: We’ve got sheaves now, so naturally we move on to morphisms between them. We begin by fixing … more »
Sheaves
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Charles wrote 5 months ago: Second in our survey of some technical tools are sheaves. Sheaves have a reputation for being terri … more »
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