Syllabus

The following is a tentative syllabus for the course. This page will be updated semi-regularly.

H = Hartshorne, B = Beauville, V = Vakil, S = Shafarevich

Lecture Date Resource Brief Description
01/04 No class (JMM)
01/06 No class (JMM)
1 01/09 H I.1 Affine varieties
2 01/11 H I.2 Projective varieties
3 01/13 H I.3 Morphisms
01/16 No class (MLK, Jr Day)
4 01/17 (x) H I.3, I.4 Morphisms and rational maps
5 01/18 H I.5, H II.1, V 2 Rational maps, nonsingular varieties, intro to sheaves
6 01/20 H II.1, V 2 Sheaves
7 01/23 V 14.2, V 15.1, S III.1.1 Line bundles
8 01/25 S III.1.1, H II.6 Divisors
9 01/27 S III.1.1, H II.6 Divisors and line bundles
10 01/30 V 19.1 Sheaf cohomology; the canonical bundle
11 01/31 (x) H IV.1 Serre duality; curves
12 02/01 H IV.1, H V.1 Curves; curves in surfaces
13 02/03 H V.1 Curves and the Picard group
14 02/06 H V.1 Adjunction and Riemann-Roch
15 02/08 H V.1 Ample bundles, Nakai-Moishezon, Hodge Index Theorem
16 02/10 H V.1 Ample bundles, Hodge Index Theorem
17 02/13 H V.3, B II.1 Blow-ups of surfaces
18 02/15 B II Birational maps and linear systems
19 02/17 B II Castelnuovo's contractibility theorem
20 02/20 H V.2, B III-IV Ruled surfaces and rational surfaces
21 02/22 B V Castelnuovo's rationality criterion
22 02/24 B VI Surfaces with geometric genus 0 and irregularity at least 1
23 02/27 B VII Kodaira dimension
24 03/01 B VIII Surfaces with Kodaira dimension 0
25 03/03 B IV Surfaces with Kodaira dimension 1
26 03/06 B X Surfaces of general type