In algebraic geometry, an affine GIT quotient, or affine geometric invariant theory quotient, of an affine scheme X = Spec ⁡ A {\displaystyle X=\operatorname...

minimal. One method for constructing the Hirzebruch surface is by using a GIT quotient:: 21  Σ n = ( C 2 − { 0 } ) × ( C 2 − { 0 } ) / ( C ∗ × C ∗ ) {\displaystyle...

{\displaystyle G/H} is a geometric quotient. A GIT quotient may or may not be a geometric quotient: but both are categorical quotients, which is unique; in other...

[X/G] The quotient stack of, say, an algebraic space X by an action of a group scheme G. X / / G {\displaystyle X/\!/G} The GIT quotient of a scheme...

{\mathfrak {g}})/\!\!/{\mathcal {G}}} is given by symplectic reduction. GIT quotient Quantization commutes with reduction Poisson–Lie group Toric manifold...

In mathematics, geometric invariant theory (or GIT) is a method for constructing quotients by group actions in algebraic geometry, used to construct moduli...

then X / / G {\displaystyle X/\!/G} (the GIT quotient of X by G) is homeomorphic to the symplectic quotient of X by a maximal compact subgroup of G. Kempf...

{\displaystyle X=\operatorname {Spec} (A)} is an affine variety, then the GIT quotient Spec ⁡ ( ( A ⊗ k ⋯ ⊗ k A ) S n ) {\displaystyle \operatorname {Spec}...

(2012), no. 4, 469--495, proposition 8 This should be understood as a GIT quotient. In a more general setting, one can speak of a weighted projective stack...

stack (roughly this is obtained by replacing the step of taking a GIT quotient by a quotient stack) Toroidal embedding Cox, David (2003), "What is a toric...

Y'} is a categorical quotient. A basic result is that geometric quotients (e.g., G / H {\displaystyle G/H} ) and GIT quotients (e.g., X / / G {\displaystyle...

theory GIT quotient Groupoid scheme Group-scheme action Group-stack Invariant theory Quotient stack Raynaud, Michel (1967), Passage au quotient par une...

geometric invariant theory (GIT), developed by David Mumford in 1965, which shows that under suitable conditions the quotient indeed exists. To see how...

group G x {\displaystyle G_{x}} , there exists an etale cover of the GIT quotient ( U , u ) → ( N x / / G x , 0 ) {\displaystyle (U,u)\to (N_{x}//G_{x}...

{\mathfrak {g}}} . We can then take the stack quotient g / G {\displaystyle {\mathfrak {g}}/G} and the GIT quotient g / / G {\displaystyle {\mathfrak {g}}/\...

\operatorname {Spec} (\mathbb {C} )} . If this is instead given by a GIT quotient, then it gives the coarse moduli space A g {\displaystyle A_{g}} . In...

semistable vector bundles using a GIT quotient. Hilbert polynomial Flat morphism Hilbert scheme Moduli space GIT quotient Grothendieck, Alexander. Techniques...

quotient of Grassmannian Gr ⁡ ( 2 , C n ) {\displaystyle \operatorname {Gr} (2,\mathbb {C} ^{n})} by the standard maximal torus. Picard variety GIT quotient...

notion depends on a choice of linearization. See also: categorical quotient, GIT quotient. Borel construction - this is an approach essentially from algebraic...

{\displaystyle {\mathcal {M}}_{g}^{0}=H_{g}^{0}/\mathrm {PGL} (5g-6)} (as a GIT quotient). If there existed multiple components of H g o {\displaystyle H_{g}^{o}}...

rings of invariants are the coordinate rings of (affine or projective) GIT quotients and they play fundamental roles in the constructions in geometric invariant...

the construction of a toric variety a step of taking GIT quotients with that of taking quotient stacks. Consequently, a toric variety is a coarse approximation...

natural GIT problem which describes that family, and so explicit examples of K-moduli of Fano threefolds can also be found as GIT quotients. For some...

spectrum of prime ideals of the ring of invariants (i.e., the affine GIT quotient). C [ Hom ⁡ ( π , G ) ] G . {\displaystyle \mathbb {C} [\operatorname...

curves. The other main technical tool are GIT quotients, since this moduli space is constructed as the quotient M g = [ U g / G L 5 g − 6 ] {\displaystyle...

singularities (e.g. a cusp) is unstable. Geometric invariant theory GIT quotient Hilbert, D. (1893), "Über die vollen Invariantensysteme (On Full Invariant...

and X ¯ {\displaystyle {\bar {X}}} is proper. Tropical geometry GIT quotient Chow quotient Toroidal embedding Tevelev, Jenia (2007-08-07). "Compactifications...

this principle is the Kempf–Ness theorem, which relates GIT quotients to symplectic quotients by showing that stable points minimize the energy functional...

Edidin and Matthew Satriano, Towards an intersection Chow cohomology for GIT quotients Fulton, William (1998), Intersection Theory, Berlin, New York: Springer-Verlag...

pertaining to basic arithmetic are recognized as operations, such as "sum", "quotient", and "cube". A sentence that assigns a value to a character starts with...