In mathematics, a moduli scheme is a moduli space that exists in the category of schemes developed by Alexander Grothendieck. Some important moduli problems of algebraic geometry can be satisfactorily solved by means of scheme theory alone, while others require some extension of the 'geometric object' concept (algebraic spaces, algebraic stacks of Michael Artin).
mathematics, a modulischeme is a moduli space that exists in the category of schemes developed by Alexander Grothendieck. Some important moduli problems of...
mathematics, in particular algebraic geometry, a moduli space is a geometric space (usually a scheme or an algebraic stack) whose points represent algebro-geometric...
completed his PhD in 1961, with a thesis entitled Existence of the modulischeme for curves of any genus. He married Erika, an author and poet, in 1959...
In algebraic geometry, a moduli space of (algebraic) curves is a geometric space (typically a scheme or an algebraic stack) whose points represent isomorphism...
scheme) X and provides techniques for forming the 'quotient' of X by G as a scheme with reasonable properties. One motivation was to construct moduli...
q {\displaystyle \mathbf {F} _{q}} and a smooth affine group scheme G over it, the moduli stack of principal bundles over X, denoted by Bun G ( X ) {\displaystyle...
_{X}:X\to \mathbb {Z} } such that if X is a quasi-projective proper modulischeme carrying a symmetric obstruction theory, then the weighted Euler characteristic...
in algebraic geometry Nakai conjecture Modulischeme – a moduli space that exists in the category of schemesPages displaying wikidata descriptions as...
generalization of algebraic spaces, or schemes, which are foundational for studying moduli theory. Many moduli spaces are constructed using techniques...
1007/BFb0091051. ISBN 978-3-540-10021-8. Chai, Ching-Li (1986). "Siegel ModuliSchemes and Their Compactifications over C {\displaystyle \mathbb {C} } ". Arithmetic...
contexts of Galois representations and moduli problems. The initial development of the theory of group schemes was due to Alexander Grothendieck, Michel...
algebraic geometry; for now see also ind-scheme). moduli See for example moduli space. While much of the early work on moduli, especially since [Mum65], put the...
{\displaystyle S} . For any scheme (or S {\displaystyle S} -scheme) X {\displaystyle X} , the X {\displaystyle X} -points of the moduli stack are the groupoid...
points collided. The Hilbert scheme Hilb ( k , d , n ) {\displaystyle \operatorname {Hilb} (k,d,n)} is the fine modulischeme of closed subschemes of dimension...
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...
\mathbb {P} _{S}^{5g-6}} . Using the standard Hilbert Scheme theory we can construct a modulischeme of curves of genus g {\displaystyle g} embedded in some...
variety Av (over the same field), which is the solution to the following moduli problem. A family of degree 0 line bundles parametrised by a k-variety T...
In mathematics, formal moduli are an aspect of the theory of moduli spaces (of algebraic varieties or vector bundles, for example), closely linked to deformation...
Noetherian, such as the Moduli of algebraic curves and Moduli of stable vector bundles. Also, this property can be used to show many schemes considered in algebraic...
{\displaystyle C,\pi :C\to \mathbf {P} ^{1}} ) where C is a smooth curve of genus g and π has degree d. Joe Harris and Ian Morrison. Moduli of curves. v t e...
(A Hilbert scheme is a scheme, but not a stack because, very roughly speaking, deformation theory is simpler for closed schemes.) Some moduli problems are...
surfaces are in this class. Gieseker showed that there is a coarse modulischeme for surfaces of general type; this means that for any fixed values of...
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