Homework: Homework will consist of bringing questions and/or
comments each week about the lectures and/or the online notes.

Summary

Algebraic curves are the most classical subject in algebraic geometry.
After introducing motivation ranging from intrinsic geometry of curves
to the geometry of moduli spaces of curves, we will focus our attention
on the subject of linear series on curves, which is essentially a fancy
way of saying maps from curves to projective spaces. Our main goal is to
discuss the use of degeneration techniques to prove important results in
the subject, but we will also discuss important auxiliary topics such
as determinantal varieties. Although many of the main results were
first stated in the 19th and early 20th century, the proofs took roughly
a century to complete, and the techniques are still evolving today. Many
of the proofs we will discuss were developed only in the past few years.

Lecture notes

The purpose of this course is to develop a set of lecture notes on the
theory of limit linear series. The current draft is posted below, and
updates will be posted as the quarter progresses.