Homework.
Liu 5.2.2, 5.2.3, 5.2.4, 5.2.7
Liu 5.2.9, 5.2.16, 5.3.2.
Hartshorne III.2.2, III.2.3, III.2,7,
Hartshorne III.3.1, III.3.2, III.3.3,
Hartshorne III.4.1, III.4.3, III.4.9,
Hartshorne III.5.1, III.5.2, III.5.3,

Apocryphal quote: "You are not an algebraic geometer till you do most exercises in Hartshorne". (János Kollár)

February self study: Hartshorne III.6: $Ext$ groups
Read about Kleiman's criterion for ampleness. Even better: read Kleiman's original paper.
April independent reaing: Hartshorne V.4, V.6

Presentations:

Enough injectives: Siddarth
$\delta$-functors: Cory
Grothendieck's dimension theorem: Jonghyun
Proposition III.3.4: Ming Hao

IV.1 Riemann-Roch: Max
IV.2 Hurwitz: Cory and Siddarth
IV.3 Embeddings: Shiyue + 1
IV.4 Elliptic curves: Max
IV.5 Canonical embedding: Shiyue + 1

V.1 surfaces: Jonghyun
V.2 Ruled surfaces: Ming Hao and Siddarth
V.3 Blowings up: Ming Hao
V.5 Birational geometry: Ming Hao