18.725 | Fall 2015 | Graduate

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

Course Info

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Fall 2015
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