it, the moduli stack of principal bundles over X, denoted by Bun G ⁡ ( X ) {\displaystyle \operatorname {Bun} _{G}(X)} , is an algebraic stack given by:...

geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric objects of some fixed kind...

algebraic geometry, the moduli stack of rank-n vector bundles Vectn is the stack parametrizing vector bundles (or locally free sheaves) of rank n over some reasonable...

{\displaystyle X} -points of the moduli stack are the groupoid of principal G m {\displaystyle \mathbb {G} _{m}} -bundles P → X {\displaystyle P\to X}...

which is the moduli stack of principal G L n {\displaystyle GL_{n}} -bundles. Since the data of a principal G L n {\displaystyle GL_{n}} -bundle is equivalent...

stratification is any of a stratification of the moduli stack of principal G-bundles by locally closed substacks in terms of "loci of instabilities". In...

Harder–Narasimhan stratification, as the moduli stack is not of finite type.) See the moduli stack of principal bundles and references therein for the precise...

semistable vector bundles and μ(W) >μ(V), then there are no nonzero maps W → V. Mumford proved that the moduli space of stable bundles of given rank and...

indefinite integrals as being examples of torsors. Beauville–Laszlo theorem Moduli stack of principal bundles Cox ring Demazure, Michel; Gabriel, Pierre...

_{l})} of the moduli stack of principal bundles is a free graded-commutative algebra on certain homogeneous generators. The original work of Michael...

the moduli stack of stable vector bundles on C {\displaystyle C} of rank r {\displaystyle r} and degree d {\displaystyle d} . It has a coarse moduli space...

sense) any natural moduli problem or, in the precise language, there is no natural moduli stack that would be an analog of moduli stack of stable curves....

One can define the moduli stack of principal bundles Bun G ⁡ ( X ) {\displaystyle \operatorname {Bun} _{G}(X)} as the quotient stack [ Ω / G ] {\displaystyle...

sheaf of rings that codifies this geometric information. Coherent sheaves can be seen as a generalization of vector bundles. Unlike vector bundles, they...

differentiable stack is the analogue in differential geometry of an algebraic stack in algebraic geometry. It can be described either as a stack over differentiable...

good-behaving moduli space of curves. 2.  A stable vector bundle is used to construct the moduli space of vector bundles. stack A stack parametrizes sets of points...

original. Teleman, Constantin (1998). "Borel–Weil–Bott theory on the moduli stack of G-bundles over a curve". Inventiones Mathematicae. 134 (1): 1–57. doi:10...

determines a morphism of schemes X →Y in a natural way. The Stacks Project, 01J5 The functor of points, Yoneda's lemmma, moduli spaces and universal properties...

language of algebraic geometry, the phase space of the system is a partial compactification of the cotangent bundle to the moduli space of stable G-bundles for...

[math.AT]. Schreiber, Urs (2011-11-16). Chern-Simons terms on higher moduli stacks (PDF). Hausdorff Institute Bonn. Schreiber, Urs (2013-10-29). Differential...

says that an algebraic stack with finite stabilizer groups has a coarse moduli space that is an algebraic space. Another type of generalization is to enrich...

instantons Gauge theory (mathematics) – Study of vector bundles, principal bundles, and fibre bundles Notes Because this projection is conformal, the...

classifying stack B G {\displaystyle BG} , the stack of principal G-bundles for a smooth linear algebraic group G. By definition, it is the quotient stack [ ∗...

construction of a corresponding complex structure. Nollet, Scott. "KODAIRA'S THEOREM AND COMPACTIFICATION OF MUMFORD'S MODULI SPACE Mg" (PDF). "Isometry of Torus"...

m_{n}} is the multiplication by n. See also: modular curve#Examples, moduli stack of elliptic curves. Siegel modular form Rigidity (mathematics) Local rigidity...

theory Pursuing Stacks Shape theory Moduli stack of formal group laws Crossed module Milnor's theorem on Kan complexes Fibration of simplicial sets May...

functor Vistoli 2008, Definition 3.10. C. Sorger, Lectures on moduli of principal G-bundles over algebraic curves Vistoli, Angelo (September 2, 2008). "Notes...

characteristic of this complex yields the correct (virtual) dimension of the quotient stack. In particular, if we look at the moduli stack of principal G {\displaystyle...

for a divisor of a local ring to be principal Scheme (mathematics) Section conjecture Semistable abelian variety Sheaf cohomology Stack (mathematics)...

This is a timeline of category theory and related mathematics. Its scope ("related mathematics") is taken as: Categories of abstract algebraic structures...