Program
Topics in Birational Geometry and Singularities
Student No.:50
Time:Wed/Thu 10:10-12:00, 2015-07-01 ~ 2015-08-12
Instructor:Yi Hu  [The University of Arizona]
Place:Conference Room 1, Floor 1, Jin Chun Yuan West Building
Starting Date:2015-7-1
Ending Date:2015-8-12
 
Description:
 
In this topics course, we will discuss some basic techniques on resolution of singularities in algebraic geometry.  Along the way we will also discuss some very interesting geometric realizations of arbitrary singularity types. We plan to cover (at least) the following topics.

1. Resolutions for singular curves. This includes various classical methods and modern techniques.

2. Resolution for surfaces. This includes many enlightening examples.

3. Resolution in characteristic zero. This provides the general method in characteristic zero and includes the idea of principalization.

4. We will also discuss the Mn\"ev Universality, a beautiful geometric realization of an arbitrary singularity type as a scheme of configurations of points in the projective plane.

5. In the first meetings, I will discuss with the students for possibly additional topics. The course is open to other related topics that the students want to learn.
 
Prerequisite:
 
One-semester course in algebraic geometry or the equivalent
 
Reference:
 
1.      Lectures on Resolution of Singularities (AM-166). János Kollár.
2.       Mnev-Sturmfels universality for schemes. R. Vakil and S. H. Lee, in "A celebration of algebraic geometry", 457-468, Clay Math. Proc., 18, Amer. Math. Soc., Providence, RI, 2013.