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)...

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...

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...

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

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...

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...

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

−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...

her work in "the dynamics and geometry of Riemann surfaces and their moduli spaces". Throughout her career, Maryam Mirzakhani achieved remarkable milestones...

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...

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

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

(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...

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

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

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...

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...

cohomology – Concept in algebraic geometry Nakai conjecture Moduli scheme – a moduli space that exists in the category of schemesPages displaying wikidata...

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...

"Dyon-monopole bound states, self-dual harmonic forms on the multi-monopole moduli space, and SL(2,Z) invariance in string theory". Physics Letters B. 329 (2):...

contribution cited for his Fields medal in 1986. Donaldson's proof utilizes the moduli space M P {\displaystyle {\mathcal {M}}_{P}} of solutions to the anti-self-duality...

"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...

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...

{\displaystyle {\overline {\mathcal {M}}}_{g,n}} be the Deligne–Mumford moduli space of curves of genus g with n marked points and M ¯ g , n ( X , A ) {\displaystyle...

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...

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...