18.727 | Spring 2008 | Graduate

Topics in Algebraic Geometry: Algebraic Surfaces

Lecture Notes

The lecture notes were prepared by Kartik Venkatram in collaboration with Professor Kumar.

1 Introduction (PDF)
2 Linear equivalence, algebraic equivalence, numerical equivalence of divisors (PDF)
3 Birational maps, rational maps, linear systems, properties of birational maps between surfaces (PDF)
4 Birational maps (cont.) (PDF)
5 Ruled surfaces I (PDF)
6 Ruled surfaces II (PDF)
7 Ruled surfaces III, rational surfaces (PDF)
8 Linear systems, rational normal scrolls (PDF)
9 Castelnuovo’s criterion for rationality (PDF)
10 Picard variety (PDF)
11 Albanese variety (PDF)
12 Non-ruled and ruled surfaces (PDF)
13 Classification of ruled surfaces (PDF)
14 Elliptic and quasi-elliptic surfaces (PDF)
15 Elliptic surfaces (cont.), Kodaira dimension 0 (PDF)
16 K3 surfaces (PDF)
17 Enriques surfaces, bielliptic surfaces (PDF)
18 Classification (PDF)
19 Elliptic/quasi-elliptic fibrations I (PDF)
20 Elliptic/quasi-elliptic fibrations II (PDF)
21 Elliptic/quasi-elliptic fibrations III, classification (PDF)
22 Classification (cont.) (PDF)
23 Moduli

Course Info

As Taught In
Spring 2008
Learning Resource Types
assignment Problem Sets
notes Lecture Notes