Tuesday, 12.30pm-1.50pm, the Tea room
Lecture 1 (December 4, 2006): Linear system of plane cubic curves through 6 points on P^2. It's image as a cubic surface in P^3 (if the points are generic). Counting constants: all cubic surfaces in P^3 can be obtained in this way. References: [1] Lecture 2 (December 11, 2006): 1. The map associated with linear system of cubics through 6 *generic* points is an embedding -- some arguments. 2. del Pezzo surfaces. cubic surface in P^3 is del Pezzo. 3. Picard group of the cubic surface -- Part 1. References: [1] Lecture 3 (January 2, 2007): Picard group of the cubic surface - Part 2. References: [1] Lectures 4-7: * 27 lines on a cubic surface. * Root system E_6, and its embedding into Pic(X). * The symmetry group of the 27 lines is isomorphic to W(E_6). ---------- References: [1] R. Hartshorne, Algebraic Geometry. [2] Griffiths, Harris. Principles of algebraic geometry. [3] Shafarevich, Algebraic surfaces (review). (EMS volume Algebraic Geometry-2) [4] Barth, Peters, Van de Ven. [5] Reid, Chapters on algebraic surfaces. [6] Mumford, Topology of normal singularities of algebraic surfaces. [7] Beauville. [8] Shafarevich, ed.-- Algebraic surfaces (Steklov's volume) [9] Manin, Cubic forms.