Algebraic Stack
In algebraic geometry, algebraic stacks are generalizations of algebraic varieties, schemes, and algebraic spaces. They were originally introduced by Deligne and Mumford (1969) to define the (fine) moduli space of genus g curves; their definition is currently referred to as Deligne–Mumford stacks. When viewed in this light, algebraic stacks are an algebraic analogue of orbifolds. They were generalized by Artin (1974) to what is now called an Artin stack. The term algebraic stack is somewhat ambiguous: it originally meant Deligne–Mumford stack, but now usually means Artin stack.
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