Math 725, Spring 2008

 

General Info:

Instructor:

Michael Temkin

E-mail: temkinsas.upenn.edu (or temkinmath.upenn.edu).

Office: DRL 4N61 (215 - 573 - 1029)

Office Hours:  by appointment

Lectures:  MW 12:00-1:30 3C6

Texts:

I will place here links to pdf files of some sources, which will change from time to time.

DM, the article by Deligne-Mumford on irreducibility of moduli spaces.

AO, lecture notes by Abramovich-Oort on de Jong’s results and related stuff.

Course description:

Our main aim is to prove de Jong’s theorem on desingularization by alterations using Hartshorne’s text as the main background. In particular, we’ll touch to some extent the following topics: stable n-pointed curves, Hilbert schemes, stacks, moduli spaces of stable n-pointed curves, stable reduction theorem and different approaches to its proof, de Jong’s theorems on semi-stable families and desingularization by alterations.

Lecture notes:

I’ll post here brief lecture notes. I’ll write down all formulations of results and definitions from past lectures. Some details about the proofs (or references to a source) will be given. Any remark on a mistake/inaccuracy will be very welcome (and I’m sure that there will be a plenty of them). Since I modify lecture notes (including the past lectures) and it can change the numeration, for example, it seems more natural not to chunk the notes by lectures, but just to post the most updated version. So, I removed the links to separate lectures.