Monthly Archives: January 2008

Papers, Readers and More

Today, rather than posting in my Algebraic Geometry from the Beginning series, I’m just going to do a quick post on a few things that are going on mathematically. First off, by clicking through Kung Fu Physics’s Super Holiday Post … Continue reading

Posted in Algebraic Geometry | 1 Comment

Morphisms of Sheaves

We’ve got sheaves now, so naturally we move on to morphisms between them. We begin by fixing a topological space and take to be two presheaves on . A morphism of presheaves is an abelian group homomorphism for each open, … Continue reading

Posted in AG From the Beginning, Algebraic Geometry | 9 Comments

Sheaves

Second in our survey of some technical tools are sheaves. Sheaves have a reputation for being terrifying and technical and some people I know have trouble seeing their purpose at all. In my opinion, they’re very nice, convenient ways to … Continue reading

Posted in AG From the Beginning, Algebraic Geometry | 4 Comments

Localization

Now that I’m settling into the semester, it’s time that I get back to rambling semi-coherently about algebraic geometry. I do, however, now have a somewhat more focused goal, and though it’s still quite a ways off, it has reminded … Continue reading

Posted in AG From the Beginning, Algebraic Geometry | 4 Comments

Tangent Spaces and Singular Points

The semester is starting up again now, so my schedule is a bit irregular. Sadly, I won’t be able to keep up the pace I set over break. However, I should still be putting out a couple of posts a … Continue reading

Posted in AG From the Beginning, Algebraic Geometry | 8 Comments

Grassmannians and Flag Varieties

Back in the second post, we defined projective space to be the collection of lines through the origin in affine space. A natural generalization is to look at -planes through the origin in affine space. At first glance, we might … Continue reading

Posted in AG From the Beginning, Algebraic Geometry, Examples | 4 Comments

The Segre Embedding

Today, we talk about the Segre Embedding. This will let us say a bit more about the products of varieties that were mentioned before.

Posted in AG From the Beginning, Algebraic Geometry, Examples | 9 Comments