Monthly Archives: April 2008

Ok, so last time, we discussed divisors. We’re going to keep going in that direction now, and now we’re going to talk about linear systems of divisors. Whenever we talk about linear systems, we’ll assume that our variety is nonsingular, … Continue reading →

Some people might say that the natural place for this topic is before talk of differential forms and of the canonical bundle, but I disagree. Well, really it’s fine either way, but this is my blog, so I’m going to … Continue reading →

We’re going to need to start out the day with a bit of algebra, because we’re going to talk about differential forms. Once we have forms, we’ll make a sheaf out of them, and then we’ll use this sheaf to … Continue reading →

We’ve now talked about vector bundles and locally free sheaves, we’re going to specify to the nicest case: rank 1. We’re generally going to ignore the distinction between the sheaf and the line bundle.

Last time, we talked about sheaves of modules, and focused on the correspondence between sheaves of ideals and subvarieties. We were talking about the internal geometry of the variety. Today, we’ll talk a bit about more external geometry. Specifically, we’ll … Continue reading →

So now that we have abstract varieties on hand, we’re going to do a bit more with sheaves, leading to some of the intimate connections between sheaf theory and geometry. Sadly, this often gives students a lot of trouble (I … Continue reading →