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

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

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

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...

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

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...

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...

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. a, b, c, d (sometimes extended to e...

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...

(1995) 109–120. P.S. Aspinwall, B.R. Greene, D.R. Morrison, "Calabi–Yau Moduli Space, Mirror Manifolds and Spacetime Topology Change in String Theory". Nuclear...

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

geometric insights with the latest algebraic techniques. He published on moduli spaces, with a theory summed up in his book Geometric Invariant Theory, on...

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...

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

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...

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

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...

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...

geometry. His particular interests concern moduli spaces, enumerative invariants associated to moduli spaces, such as Gromov–Witten invariants and Donaldson–Thomas...

{\displaystyle {\mathcal {M}}_{1,1}} to the affine line, the coarse moduli space of elliptic curves, given by the j-invariant of an elliptic curve. It...

theory gives a moduli space of cubic surfaces, with one point for each isomorphism class of smooth cubic surfaces. This moduli space has dimension 4...

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...

"moduli space" of the torus to contain one point for each conformal equivalence class, with the appropriate topology. It turns out that this moduli space...

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...

3, the number of moduli of a curve of genus g, unless g is 2. Much more is known about the hyperelliptic locus in the moduli space of curves or abelian...

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...

algebraic equation satisfied by moduli, in the sense of moduli problems. That is, given a number of functions on a moduli space, a modular equation is an equation...