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theory. The nerve of a category is often used to construct topological versions of moduli spaces. If X is an object of C, its moduli space should somehow...

In algebraic geometry, the moduli stack of rank-n vector bundles Vectn is the stack parametrizing vector bundles (or locally free sheaves) of rank n over...

In mathematics, a Higgs bundle is a pair ( E , φ ) {\displaystyle (E,\varphi )} consisting of a holomorphic vector bundle E and a Higgs field φ {\displaystyle...

of various moduli spaces of holomorphic polygons correspond to configurations of degenerate polygons. This definition of Fukaya category for a general...

{\displaystyle {\overline {\mathcal {M}}}_{g,n}} be the Deligne–Mumford moduli space of curves of genus g {\displaystyle g} with n {\displaystyle n} marked...

values in categories rather than sets. Stacks are used to formalise some of the main constructions of descent theory, and to construct fine moduli stacks...

Quiver representations in toric geometry Projective toric varieties as fine moduli spaces of quiver representations Wikimedia Commons has media related to...

homeomorphisms from S {\displaystyle S} to itself. It can be viewed as a moduli space for marked hyperbolic structure on the surface, and this endows it...

conditions are used in the construction of the moduli stack of elliptic curves and the construction of the moduli stack of pointed curves. Throughout this article...

on a stability condition on the derived category D b ( M ) {\displaystyle D^{b}({\mathcal {M}})} of the moduli spaces being studied. Essentially, these...

In mathematics, a pair of pants is a surface which is homeomorphic to the three-holed sphere. The name comes from considering one of the removed disks...

the lack of moduli interpretations of those compactifications; i.e., they do not represent (in the category-theory sense) any natural moduli problem or...

closures intersect are identified in the moduli space. These moduli spaces are called the Dolbeault moduli spaces. Notice that by setting Φ = 0 {\displaystyle...

the theory of four-manifolds in algebraic topology, and to the theory of moduli spaces in algebraic geometry. Donaldson, Jones, Witten, and Kontsevich have...

{G} _{m}} is the moduli space of line bundles, so the line bundle L → S {\displaystyle L\to S} corresponds to an object of the category B G m ( S ) {\displaystyle...

integral Differential of the first kind Jacobian variety Generalized Jacobian Moduli of algebraic curves Hurwitz's theorem on automorphisms of a curve Clifford's...

of a given type can itself be viewed as a variety or scheme, known as a moduli space. For some of the detailed definitions in the theory of schemes, see...

^{2})} above), since they act on Teichmüller space and the quotient is the moduli space of Riemann surfaces homeomorphic to the surface. These groups exhibit...

to determine if it is stable or not. This forms the basis for studying moduli of stable vector bundles in many specific cases, such as on principally...

states of type IIA theories compactified on X, especially 0-branes that have moduli space X. It is known that all of the BPS states of type IIB theories compactified...