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In mathematics a stack or 2-sheaf is, roughly speaking, a sheaf that takes 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 when fine moduli spaces do not exist.
The Stacks Project is an open source collaborative mathematics textbook writing project with the aim to cover "algebraic stacks and the algebraic geometry needed to define them".
Stack (geology), a large vertical column of rock in the sea; Stack (mathematics), a sheaf that takes values in categories rather than sets; Algebraic stack, a special kind of stack commonly used in algebraic geometry Stacks Project, an open source collaborative mathematics textbook writing project
An effective quotient orbifold, e.g., [/] where the action has only finite stabilizers on the smooth space , is an example of a quotient stack. [2]If = with trivial action of (often is a point), then [/] is called the classifying stack of (in analogy with the classifying space of ) and is usually denoted by .
Shqip; Sicilianu ... Mathematics is a field of study that discovers and organizes methods, theories and theorems that are developed and proved for the needs of ...
In mathematics, an algebraic stack is a vast generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory.Many moduli spaces are constructed using techniques specific to algebraic stacks, such as Artin's representability theorem, which is used to construct the moduli space of pointed algebraic curves, and the moduli stack of elliptic curves.
It is a classical observation that every elliptic curve over is classified by its periods.Given a basis for its integral homology , (,) and a global holomorphic differential form (,) (which exists since it is smooth and the dimension of the space of such differentials is equal to the genus, 1), the integrals [] = [] give the generators for a -lattice of rank 2 inside of [1] pg 158.
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.