18.727 | Spring 2008 | Graduate

Topics in Algebraic Geometry: Algebraic Surfaces

Calendar

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

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Spring 2008
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