In algebraic geometry, a Deligne–Mumford stack is a stack F such that the diagonal morphism F → F × F {\displaystyle F\to F\times F} is representable,...

extensions Deligne torus Deligne–Lusztig theory Deligne–Mumford moduli space of curves Deligne–Mumford stacks Fourier–Deligne transform Deligne cohomology...

⊆ Deligne–Mumford stacks ⊆ algebraic stacks (Artin stacks) ⊆ stacks. Edidin (2003) and Fantechi (2001) give a brief introductory accounts of stacks, Gómez...

to be a Deligne–Mumford stack. The subclass of Deligne-Mumford stacks is useful because it provides the correct setting for many natural stacks considered...

group Mumford measure Mumford vanishing theorem Theta representation Manin–Mumford conjecture Horrocks–Mumford bundle Deligne–Mumford moduli space of stable...

quotient stacks (e.g., a Deligne–Mumford stack.) A quotient stack is also used to construct other stacks like classifying stacks. A quotient stack is defined...

{\mathcal {M}}_{g}} . Using deformation theory, Deligne and Mumford show this stack is smooth and use the stack of isomorphisms between stable curves I s o...

{\displaystyle {\mathcal {M}}_{1,1}} . The moduli stack of elliptic curves is a smooth separated Deligne–Mumford stack of finite type over Spec ( Z ) {\displaystyle...

compatibility conditions among F ξ {\displaystyle F_{\xi }} 's. For a Deligne–Mumford stack, there is a simpler description in terms of a presentation U → X...

In algebraic geometry, given a Deligne–Mumford stack X, a perfect obstruction theory for X consists of: a perfect two-term complex E = [ E − 1 → E 0 ]...

vector bundle stack V {\displaystyle {\mathcal {V}}} on a Deligne–Mumford stack X is a group-stack such that there is a vector bundle V over k on X and a...

"Riemann-Roch Theorems for Deligne-Mumford Stacks". arXiv:math/9803076. Toen, Bertrand (1999-08-18). "K-theory and cohomology of algebraic stacks: Riemann-Roch theorems...

fact (in a nice case), a Deligne–Mumford stack. Conversely, any DM stack is of this form. Simplicial scheme Algebraic stacks, Ch 3. § 1. Gillet 1984....

algebraic spaces. More general than an algebraic space is a Deligne–Mumford stack. DM stacks are similar to schemes, but they permit singularities that...

Jean-Louis Verdier (co-founder of the derived category theory), and Pierre Deligne. Collaborators on the SGA projects also included Michael Artin (étale cohomology)...

before the notion of moduli stack was invented. In fact, the idea of a moduli stack was invented by Deligne and Mumford in an attempt to prove the projectivity...

of ringed topoi, besides ringed spaces, are the étale topoi of Deligne–Mumford stacks. Michael Artin and Barry Mazur associated to the site underlying...

basic theory (mostly over Q) for the Chow group of a (separated) Deligne–Mumford stack. There, the Chow group is defined exactly as in the classical case:...

{X}}} over a field k is a smooth proper geometrically connected Deligne–Mumford stack of dimension 1 over k that contains a dense open subscheme. A stacky...

be used to construct examples of orbifolds, or Deligne–Mumford stacks. Étale morphism Orbifold Stack (mathematics) Dimca, Alexandru (1992), Singularities...

of algebraic stacks (or "Artin stacks"), which can be considered geometric objects. These include Deligne–Mumford stacks (similar to orbifolds in topology)...

embedding of X into the normal cone. Let X {\displaystyle X} be a Deligne–Mumford stack locally of finite type over a field k {\displaystyle k} . If L X...

to stacks in the sense of Grothendieck, usually with some additional representability conditions, leading to Artin stacks and, even finer, Deligne–Mumford...

(2008-04-13). "Gromov-Witten theory of Deligne-Mumford stacks". arXiv:math/0603151. Cadman, Charles (2007). "Using stacks to impose tangency conditions on curves"...

{O}}_{X}|_{U}} . orbifold Nowadays an orbifold is often defined as a Deligne–Mumford stack over the category of differentiable manifolds. p-divisible group...

to stacks in the sense of Grothendieck, usually with some additional representability conditions leading to Artin stacks and, even finer, Deligne–Mumford...

¯ g {\displaystyle {\overline {\mathcal {M}}}_{g}} is a smooth Deligne–Mumford stack, he considered a covering by a scheme M ~ g → M ¯ g {\displaystyle...

the stack of partial stabilizations of prestable curves. (2013) Bulletin of the London Mathematical Society, 45(1):93-102. On the geometry of Deligne-Mumford...

work over the moduli stack of smooth elliptic curves, and they also work for the Deligne-Mumford compactification of this moduli stack, in which elliptic...

construct an intersection theory of Deligne–Mumford stacks Schottky problem Siegel modular variety Moduli stack of elliptic curves Moduli of algebraic...