Monthly Archives: April 2008

Next Topic and Hiatus

Ok, so with the overwhelming majority of one vote, the next thing I talk about will be algebraic surfaces and intersection theory.  However, first I need to do a bit of reading on this topic, as well as finishing up … Continue reading

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Ok, now I’m annoyed

I’ve generally been well-behaved about focusing on the math on this blog rather than going off into politics or whatever, but sometime while I was at my office today, someone went around campus and put up posters for Ben Stein’s … Continue reading

Posted in Uncategorized | 5 Comments

Linear Systems

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

Posted in AG From the Beginning, Algebraic Geometry | 7 Comments

Weil Divisors, Cartier Divisors and more Line Bundles.

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

Posted in AG From the Beginning, Algebraic Geometry | 7 Comments

Differential Forms and the Canonical Bundle

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

Posted in AG From the Beginning, Algebraic Geometry | 12 Comments

Line Bundles and the Picard Group

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.

Posted in AG From the Beginning, Algebraic Geometry | 12 Comments

Locally Free Sheaves and Vector Bundles

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

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