Deligne–Mumford Stack
A Deligne–Mumford stack admits a surjective étale atlas by a scheme. Compare its atlas condition with the smooth atlas used for general algebraic stacks, using the discussion of stable curves to orient further reading.
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Where to read
Start here: The Stacks Project — Algebraic stacks
The Stacks Project Authors · Online reference · English · Free full text
Section 94.12, Definition 94.12.2 and the preceding discussion of Deligne–Mumford and Artin stacks
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Algebraic Geometry in the library · Preparation and skip guidance