Lecture Notes

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

All lecture notes in one file: 18.725 Lecture Notes (PDF)

Course Info