# 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.

syllabus

#### 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. Laz1.ps (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

#### Homeworks:

hw1 hw2 hw3
hw4