Algebraic Learning Seminar

University of Colorado Boulder

Spring 2026: Algebraic Stacks and Moduli Spaces

We will be learning about algebraic stacks and their applications in studying moduli spaces of varieties with a focus towards understanding the moduli of stable curves.

References:

Stacks for Everybody by Fantechi
Moduli and Stacks by Alper
Introduction to stacks and moduli UW Zoom lectures by Alper
Moduli of Curves by Harris and Morrison
An introduction to moduli stacks, with a view towards Higgs bundles on algebraic curves by Yano and Jonathan
Stacks Project by Johan DeJong

Meetings:

We will meet once a week to discuss the reading and work on problems. Location/dates are TBD

Schedule:

The following is an ambitious schedule and will change as needed.

Instead of listing chapters in Alper, we'll instead follow his lectures and use his book as supplement. To quote his preface,

This book is long (sorry!) and you should not read it linearly from start to finish. The hope is that each chapter and even each section can be read independently, and that the reader can skip around as desired.

So the plan will be to watch his lectures and then read his book as supplement.

Week 0: No meeting

Week 1: Fantechi

Week 2: Alper Lecture 1, Lecture 2

Week 3: Lecture 3

Week 4: Lecture 4

Week 5: Lecture 5, Lecture 6

Week 6: Lecture 7

Week 7: Lecture 8

Week 8: Lecture 9, Lecture 10

Week 9: Lecture 11

Week 10: Lecture 12, Lecture 13