1.1 Main References

1. Bădescu, Algebraic surfaces  [ 2 ] . This is the main text I want to try to work through. There are two advantage over Beauville’s book: (1) the goal is to explain things in arbitrary characteristic, (2) it works in a way that seems closer in spirit to the methods of the minimal model program (MMP) for higher dimensional varieties. On the other hand, it is also somewhat more demanding on the reader.

2. Beauville, Complex algebraic surfaces  [ 1 ] . This is another nice book on algebraic surfaces focusing on the complex case.

3. Fulton, Intersection Theory  [ 3 ] . The books by Bădescu and Beauville use an ad hoc version of the numerical part of intersection theory, which I believe first appeared in Kleiman’s paper  [ 5 ] . I want to try to explain a little bit of Fulton’s Intersection Theory because I think that is the version that is more likely to be remembered.

4. Hartshorne, Algebraic geometry  [ 4 ] .

5. Kleiman, Towards a Numerical Theory of Ampleness  [ 5 ] .

6. Lazarsfeld, Positivity in algebraic geometry I and II  [ 6 , 7 ] .