Algebraic Surfaces
Lectures started on April, 16. Starting April 21, the course takes place on
Wednesday, from 13:15-14:45 in 3.007 (RUD25).
Contents
| Date | Subject |
|---|---|
| April, 16 | Introduction + Classification of curves. |
| April, 21 | Divisors on curves, Riemann-Roch for curves |
| April, 28 | Cohomology of sheaves |
| May, 5 | Intersection pairing on Div(S) |
| May, 12 | Riemann-Roch for surfaces. |
| May, 19 | No lecture |
| May, 26 | Hodge Theory; Nef-cone |
| June, 2 | Nef-cone, ample-cone and Nakai-Moishezon |
| June, 9 | Sigma-process I |
| June, 11 | Extra lecture (instead of May, 19) in 1.023 Sigma-process II |
| June, 16 | Ruled surfaces I |
| June, 23 | Ruled surfaces II |
| June, 30 | Stein factorization, Albanese Torus and Kodaira dimension |
| July, 7 | Statement of the Enriques-Kodaira classification |
| July, 9 | Extra lecture (instead of July, 14) in 1.023 K3 surfaces and Elliptic surfaces |
| July, 14 | No lecture |
Literature
| A. Beauville | Complex Algebraic Surfaces (Cambridge University Press) |
| K. Hulek | Algebraische Flächen (Lecture Notes (German, pdf)) |
| W. Barth, K. Hulek, C.A.M. Peters, A. Van de Ven | Compact Complex Surfaces (2nd Edition) |
| R. Hartshorne | Algebraic Geometry (Chapter V) |
| R. Miranda | An Overview of Algebraic surfaces (Lecture Notes (ps)) |
| R. Miranda | Elliptic Surfaces |
| M. Reid | Reid - Chapters on Algebraic Surfaces (Course notes) |