Algebraic Geometry

Calendar

SES #	TOPICS	KEY DATES
1	Course Introduction, Zariski Topology
2	Affine Varieties	Problem Set 1 due
3	Projective Varieties, Noether Normalization
4	Grassmannians, Finite and Affine Morphisms	Problem Set 2 due
5	More on Finite Morphisms and Irreducible Varieties
6	Function Field, Dominant Maps	Problem Set 3 due
7	Product of Varieties, Separatedness
8	Product Topology, Complete Varieties	Problem Set 4 due
9	Chow’s Lemma, Blowups
10	Sheaves, Invertible Sheaves on P1
11	Sheaf Functors and Quasi-coherent Sheaves	Problem Set 5 due
12	Quasi-coherent and Coherent Sheaves
13	Invertible Sheaves	Problem Set 6 due
14	(Quasi)coherent Sheaves on Projective Spaces
15	Divisors and the Picard Group
16	Bezout’s Theorem	Problem Set 7 due
17	Abel-Jacobi Map, Elliptic Curves
18	Kähler Differentials	Problem Set 8 due
19	Smoothness, Canonical Bundles, the Adjunction Formula
20	(Co)tangent Bundles of Grassmannians	Problem Set 9 due
21	Riemann-Hurwitz Formula, Chevalley’s Theorem
22	Bertini’s Theorem, Coherent Sheves on Curves
23	Derived Functors, Existence of Sheaf Cohomology	Problem Set 10 due
24	Birkhoff–Grothendieck, Riemann-Roch, Serre Duality
25	Proof of Serre Duality	Problem Set 11 due