This is a list of what we covered in each lecture, along with a reference for what material to read to catch up if you missed the lecture. All section numbers are by default references to the course text (Artin's manuscript). For anything we cover that isn't in that book, I'll provide other references or written notes.

References to [Vakil] are to Ravi Vakil's excellent introductory book on algebraic geometry via scheme theory, which can be found at https://math.stanford.edu/~vakil/216blog/FOAGaug2922public.pdf.

Lecture date	Topics covered	References
Feb 6	Affine and projective varieties,	1.1-1.3
Feb 8	Tangent lines and singularities	1.4, 1.7
Feb 15	Dual curve	1.5
Feb 22	Resultants, Discriminants, Bezout's theorem, Plücker formulae	1.6, 1.9-1.10
Feb 27	Nullstellensatz, Spectrum of a ring, Zariski topology	2.1-2.4, our proof of the Nullstellensatz can be found in Section 11.8.6 of Artin's book Algebra, second edition.
Feb 29	Morphisms of varieties, open and closed embeddings	2.5-2.6
Mar 5	Projective varieties, regular & rational functions, the structure sheaf	3.1-3.2, 3.4, 6.1
Mar 7	Morphisms of varieties, Product varieties	3.3, 3.5-3.6, see [Vakil] 5.3 for a discussion of the affine communication lemma (in the context of schemes)
Mar 12	Finite and integral morphisms, Nakayama's Lemma, Noether normalization, normalization	4.1-4.3
Mar 14	More on normalization, dimension	4.3-4.5
Mar 19	Fiber dimension, Grassmannian, incidence correspondences	5.6, 3.7
Mar 21	27 lines, local rings of curves	4.7, 5.1-5.2
Apr 2	Smooth curves, Chevalley's theorem	5.2-5.4
Apr 4	Proper varieties, divisors, quasicoherent sheaves	5.5, 8.1.4-8.1.9, 6.1-6.3
Apr 9	Examples of quasicoherent sheaves, sheaves O(n) on projective space	6.4, 6.7
Apr 11	More on quasi-coherent sheaves	6.5-6.6
Apr 16	Cohomology: Construction and properties	7.1-7.4 (Note: We take a different approach to the construction, following [Vakil] 19.2. However, the specific construction will not matter for the rest of the class.)
Apr 18	Cohomology of sheaves on projective space	7.5, 7.7
Apr 23	Bezout's theorem, divisors, Riemann-Roch	7.8, 8.1, 8.2
Apr 25	More on Riemann-Roch	8.7, 8.8
Apr 30	(Minh-Tam) Weierstrass form, Pic
May 2	(Minh-Tam) Weierstrass uniformization, complex analytic description of Pic