In mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent...

In algebraic geometry, a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism...

more specifically, moduli space is borrowed from algebraic geometry), where it is used synonymously with "parameter". The word moduli (Moduln in German)...

her work in "the dynamics and geometry of Riemann surfaces and their moduli spaces". Mirzakhani was considered a leading force in the fields of hyperbolic...

of the equations are called Yang–Mills connections or instantons. The moduli space of instantons was used by Simon Donaldson to prove Donaldson's theorem...

moduli spaces will be not just topological spaces, but have some additional structure. For example, the Dolbeault moduli space and Betti moduli space...

−2.) The moduli space of quasi-polarized K3 surfaces of genus g is still irreducible of dimension 19 (containing the previous moduli space as an open...

parabola. That is, they specify coordinates on the 'space of parabolas': this is known as a moduli space of parabolas. Lambda calculus Observable variable...

Quadratic space Quotient space (disambiguation) Riemann's Moduli space Sample space Sequence space Sierpiński space Sobolev space Standard space State space Stone...

monopole moduli space is a space parametrizing monopoles (solutions of the Bogomolny equations). Atiyah and Hitchin (1988) studied the moduli space for 2...

constructions of descent theory, and to construct fine moduli stacks when fine moduli spaces do not exist. Descent theory is concerned with generalisations...

deformation theory of the first order should equate the Zariski tangent space with a moduli space. The phenomena turn out to be rather subtle, though, in the general...

an isometry of the images of the mapping.: 121 : 225  Generally, the moduli space of a faithful realization of an abstract polytope is a convex cone of...

this way Teichmüller space can be viewed as the universal covering orbifold of the Riemann moduli space. The Teichmüller space has a canonical complex...

of which the kinetic part coincides with the Kähler potential of the moduli space of vacua. Before taking the low-energy effective action, the theory is...

(that is, the fiber is a 2-dimensional vector space). The rank 2 vector bundle arises as the solution space to Hitchin's equations for a principal SU(2)...

Grothendieck–Riemann–Roch can be used in proving that a coarse moduli space M {\displaystyle M} , such as the moduli space of pointed algebraic curves M g , n {\displaystyle...

pants are used to construct the Fenchel-Nielsen coordinates on Teichmüller space, and in topological quantum field theory where they are the simplest non-trivial...

topology of the moduli space of SU(2) instantons over a 4-sphere. They showed that the natural map from this moduli space to the space of all connections...

manifold in four dimensions. In this work the moduli space of self-dual connections (instantons) on Euclidean space was studied, and shown to be of dimension...

where it is the correct stability condition to allow the formation of moduli spaces, and where it precisely characterises the existence of Kähler–Einstein...

moduli spaces of solutions of the Seiberg–Witten equations tends to be compact, so one avoids the hard problems involved in compactifying the moduli spaces...

studying the tangent space of a point of the moduli space of all solutions. Ideally one would like to describe the (moduli) space of all solutions explicitly...

upper half space Siegel modular form, a type of automorphic form defined on the Siegel upper half-space Siegel modular variety, a moduli space constructed...

often used to construct topological versions of moduli spaces. If X is an object of C, its moduli space should somehow encode all objects isomorphic to...

04879. doi:10.1112/blms/bdp106. S2CID 1070427. Reid, Miles (1987). "The Moduli space of 3-folds with K = 0 may nevertheless be irreducible". Mathematische...

In algebraic geometry, a moduli scheme is a moduli space that exists in the category of schemes developed by French mathematician Alexander Grothendieck...

varieties through the minimal model program and the construction of moduli spaces sets the field apart from differential geometry, where the classification...

{Z} )} , there is a moduli space of principally polarised abelian varieties given as a stacky quotient of Siegel upper half-space by the symplectic group...

the torus). To obtain the analytic moduli space (forgetting the marking) one takes the quotient of Teichmüller space by the mapping class group. In this...