In the Spring Semester of 2010, I am organizing a seminar on Algebraic Surfaces. Currently, our plan is to come together every Thursday, starting 11 February.
We will treat the Enriques classification of algebraic surfaces over the complex numbers, or equivalently, over any algebraically closed field of characteristic zero. We intend to give complete proofs of all the results presented in the seminar, assuming a basic knowledge of algebraic geometry, as well as a good understanding of sheaf theory and its use in algebraic geometry. Also, attention will be paid to the various types of surfaces we will encounter along the way. Our main source will be the book by Beauville, listed below.
The Enriques classification says that any smooth projective algebraic surface belongs to one or more of the following types: rational surfaces, ruled surfaces, K3 surfaces, abelian surfaces, bielliptic (also known as hyperelliptic) surfaces, Enriques surfaces, elliptic surfaces and surfaces of general type. A more precise classification can be made in terms of the Kodaira dimension, the Hodge numbers and the plurigenera of a surface. These will all be defined during the seminar.
If time permits, we can also look at other topics, for instance: arithmetic aspects (e.g. the existence of rational points on surfaces and obstructions to this), the Enriques classification in characteristic p due to Mumford and Bombieri, and the Enriques-Kodaira classification of all compact complex-analytic varieties of complex dimension 2. We will let the choice of these optional topics depend on the wishes of the participants. If you have any requests, please let me know!
February 11th, 2010. Room 405.
February 25th, 2010. Room 405.
March 18th, 2010. Room 405.
March 25th, 2010. Room 405.
April 1st, 2010. Room 405.
April 8th, 2010. Room 312.
April 15th, 2010. Room 405.
April 22nd, 2010. Room 405.
May 6th, 2010. Room 312!