Math Notes

University Mathematics

Algebraic Stacks

Algebraic Stacks

Concepts

Algebraic (Artin) Stacks Deligne--Mumford Stacks Quotient Stacks $[X/G]$Gerbes and Root Stacks Coarse Moduli Spaces

Theorems

Artin Representability Theorem Keel--Mori Theorem: Existence of Coarse Moduli Spaces Quotient Singularities: Resolution and McKay Correspondence Chow's Lemma for Stacks

Proofs

Proof of the Artin Representability Theorem Proof that $[X/G]$ is an Algebraic Stack

Mathematics Lecture Notes