2006: Algebraic surfaces-2

Algebraic surfaces - 2

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.