Algebraic Surfaces

NB: most documents are in pdf format. You might need Acrobat Reader (which is free to download) to view it. Some version of GhostView also works.


Lecture Notes:

Lecture 1: Review on compact Riemann surfaces/ algebraic curves.

Lecture 2: Affine varieties and projective varieties.

Lecture 3: Divisors.

Lecture 4: Linear series and maps to projective spaces.

Here is some part of Lazarsfeld's Positivity in Algebraic Geometry, which defines divisors and linear series. (It's in postscript, you might need GhostView)

Lecture 5: Sheaves cohomology.

Lecture 6: Bertini's theorem, Ampleness Criterion, Intersection theory and Riemann-Roch theorem on surfaces.

Lecture 7: Hodge Index Theorem

Lecture 8: Blowing-up and Blowing-down

Lecture 9: Birational maps and minimal models

Lecture 10: Minimal model program for surfaces

Lecture 11: rational surfaces

Lecture 12: ruled surfaces


hw1    hw2    hw3    hw4