Category Archives: Deformation Theory

Monodromy and Moduli

Posted on March 2, 2010 by Charles Siegel

Today, we’re going to prove a BIG theorem, but only in the characteristic zero case (we’ll be working over as usual). The theorem is rather tough, and to do it in positive characteristics it’s best done through stacks. Specifically, we’ll … Continue reading →

Posted in Algebraic Geometry, Algebraic Topology, Big Theorems, Curves, Deformation Theory, Moduli of Curves | 3 Comments

Deligne and Mumford on the Moduli of Curves

Posted on February 18, 2009 by Charles Siegel

Today I’m going to talk a bit about an important paper from 1969.  This one.  It’s a bit hard to read at some points, but it was revolutionary.  In it, Pierre Deligne and David Mumford prove that the moduli space … Continue reading →

Posted in Algebraic Geometry, Big Theorems, Curves, Deformation Theory | 3 Comments

Examples of Moduli Spaces

Posted on July 23, 2008 by Charles Siegel

Now we’re done constructing , so it’s time to get the general Hilbert scheme done, and then to construct some other moduli spaces. Now, as , we can see that is a subfunctor of , so we want to try … Continue reading →

Posted in AG From the Beginning, Algebraic Geometry, Deformation Theory, Examples, Hilbert Scheme | 3 Comments

The Hilbert Scheme

Posted on July 18, 2008 by Charles Siegel

Now that we have a notion of moduli space, we’re going to look at several concrete examples. I mentioned that the Grassmannian is a fine moduli space for -planes in . We’ll make use of this to construct several more. … Continue reading →

Posted in AG From the Beginning, Algebraic Geometry, Deformation Theory, Examples, Hilbert Scheme | 17 Comments

Moduli Spaces and Base Change

Posted on July 17, 2008 by Charles Siegel

Last time we spoke of representable functors and talked about how to check if a functor is representable. The whole idea being that if we can first construct a functor that SHOULD be the functor of points for the scheme … Continue reading →

Posted in AG From the Beginning, Algebraic Geometry, Deformation Theory | 1 Comment