MA 746, ALGEBRAIC GEOMETRY, SPring 2022

Overview

We will bring to life the abstract theory of schemes with the beautiful phenomena which appear in dimensions 1 and 2.

Topics (not necessarily exhaustive)

Riemann surfaces and the Riemann existence theorem

Divisors and the Riemann-Roch theorem

Curves of genus 0 (over a non-algebraically closed field)

Elliptic curves and their moduli

The Abel-Jacobi theorem

Moduli spaces of curves

Basic surfaces: Rational, Ruled, del Pezzo

The 27 lines on a cubic surface

Surface singularities

Elliptic surfaces: NĂ©ron-Severi and Mordell-Weil lattices

K3 surfaces

Expectations

If you are taking this class for credit, I expect you to attend class. By the end of the semester, I'd like you to write a short exposition (10-20 pages) of one of the topics we cover.