Monthly Archives: November 2010

Prym Varieties

Let be an unramified double cover, where is geneus . Then has genus by the Riemann-Hurwitz formula. Now, encodes lots of information about the geometry of , especially with the additional data of the theta divisor. It turns out that … Continue reading

Posted in Abelian Varieties, AG From the Beginning, Algebraic Geometry, Cohomology, Curves, Examples, Hodge Theory, MaBloWriMo | Leave a comment

Rational Normal Scrolls

Today, we’re going to talk about a very important class of rational varieties, that show up all the time, in quite a variety of different contexts, and at the end, we’ll talk about why.

Posted in AG From the Beginning, Algebraic Geometry, Examples, MaBloWriMo | Leave a comment

Determinantal Varieties

Let be the projectivization of . Then for all , we have a variety given as the set of matrices of rank at most , which is given by the vanishing of the determinents of minors. We call these the … Continue reading

Posted in AG From the Beginning, Algebraic Geometry, Examples, MaBloWriMo | Leave a comment

Technology Survey!

I know I still have a few readers out there, and some of you are probably technophiles, so here’s a question: I’ve been considering switching from live-texing of things to a digital pen of some sort.  Anyone have any experience … Continue reading

Posted in Uncategorized | 9 Comments

Low Genus Moduli of Curves

Pretty much everything in this post is in Mumford’s “Curves and their Jacobians,” but I do a couple of things slightly differently, and I intend to supply a bit more detail in some places.  The goal here is to construct … Continue reading

Posted in AG From the Beginning, Algebraic Geometry, Curves, Examples, MaBloWriMo, Moduli of Curves | 3 Comments

The Stanley-Reisner Ring

Today, we’re going to do something completely different, but which most of my peers seem not to have seen, but is a very cool application of algebraic geometry.

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

A short post on bitangents

Today’s post will be, as the title says, a bit short.  It will, more-or-less finish our current discussion of theta characteristics, and then we’ll get back to something else.  But we’ll derive a nice case of a classical formula.

Posted in AG From the Beginning, Algebraic Geometry, Curves, Enumerative Geometry, Examples, MaBloWriMo | 1 Comment