Student Algebraic Geometry

We will give an introduction to the classification of surfaces and 2d minimal model programme with a focus on low characteristic.

Introduction to the topic and proof that there is no elliptic curve over the integers using Weierstrass equations.

The refined patchworking theorem (Section 2.5.10–11 of [IMS09])

A refinement of the tropical limit (Section 2.5.8–9 of [IMS09])

Construction of the tropical limit (Section 2.5.4–5 of [IMS09])

Statement of the problem (Section 2.5.1–3 of [IMS09]), small examples

Patchworking with singularities (Section 2.4 of [IMS09])

Examples of patchworking (Section 2.3.3–4 of [IMS09]), if time permits, dealing with non-convex triangulations (Section 2.3.5 of [IMS09])

The statement and proof of the patchworking theorem (Section 2.3.1–2 of [IMS09])

Other facts about toric varieties that we need (Chapter 2.2.4–6 of [IMS09]), if time permits, other topics (Chapter 2 of [Ful93])