Geometric space whose points represent algebro-geometric objects of some fixed kind
In mathematics, in particular algebraic 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, or isomorphism classes of such objects. Such spaces frequently arise as solutions to classification problems: If one can show that a collection of interesting objects (e.g., the smooth algebraic curves of a fixed genus) can be given the structure of a geometric space, then one can parametrize such objects by introducing coordinates on the resulting space. In this context, the term "modulus" is used synonymously with "parameter"; moduli spaces were first understood as spaces of parameters rather than as spaces of objects. A variant of moduli spaces is formal moduli. Bernhard Riemann first used the term "moduli" in 1857.[1]
^Chan, Melody. "Moduli Spaces of Curves: Classical and Tropical" (PDF). AMS.
In mathematics, in particular algebraic geometry, a modulispace is a geometric space (usually a scheme or an algebraic stack) whose points represent...
In algebraic geometry, a modulispace 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 modulispace of a faithful realization of an abstract polytope is a convex cone of...
her work in "the dynamics and geometry of Riemann surfaces and their modulispaces". On 14 July 2017, Mirzakhani died of breast cancer at the age of 40...
geometric insights with the latest algebraic techniques. He published on modulispaces, with a theory summed up in his book Geometric Invariant Theory, on...
monopole modulispace is a space parametrizing monopoles (solutions of the Bogomolny equations). Atiyah and Hitchin (1988) studied the modulispace for 2...
topology of the modulispace of SU(2) instantons over a 4-sphere. They showed that the natural map from this modulispace to the space of all connections...
studying the tangent space of a point of the modulispace of all solutions. Ideally one would like to describe the (moduli) space of all solutions explicitly...
absolute value of a real or complex number ( |a| ) Modulispace, in mathematics a geometric space whose points represent algebro-geometric objects Conformal...
{\displaystyle {\mathcal {M}}_{1,1}} to the affine line, the coarse modulispace of elliptic curves, given by the j-invariant of an elliptic curve. It...
"Dyon-monopole bound states, self-dual harmonic forms on the multi-monopole modulispace, and SL(2,Z) invariance in string theory". Physics Letters B. 329 (2):...
the torus). To obtain the analytic modulispace (forgetting the marking) one takes the quotient of Teichmüller space by the mapping class group. In this...
"modulispace" of the torus to contain one point for each conformal equivalence class, with the appropriate topology. It turns out that this moduli space...
with an integration over the space of all possible complex structures modulo diffeomorphisms, which is simply the modulispace of the given topological surface...
algebraic equation satisfied by moduli, in the sense of moduli problems. That is, given a number of functions on a modulispace, a modular equation is an equation...
vast generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory. Many modulispaces are constructed using techniques...
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