# Friday, July 30

References:

- Course website: <https://sites.math.washington.edu/~jarod/math582C.html>
- [Gómez 99: Expository article on algebraic stacks](https://arxiv.org/pdf/math/9911199.pdf)


:::{.remark}
Stated goal of the course: prove that the moduli space $\bar{\mg}$ of stable curves (for $g\geq 2$) is a smooth, proper, irreducible Deligne-Mumford stack of dimension $3g-3$.
Moreover, it admits a projective coarse moduli space.

In the process we'll define **algebraic spaces** and **stacks**.

Prerequisites:

- Schemes
- Existence of Hilbert schemes
- Artin approximation
- Resolution of singularities for surfaces
- Deformation theory

:::