Topic
Moduli scheme
About: Moduli scheme is a research topic. Over the lifetime, 173 publications have been published within this topic receiving 8388 citations.
Papers published on a yearly basis
Papers
Book•
1 Jan 1965
TL;DR: Geometric invariant theory for moduli spaces has been studied extensively in the mathematical community as mentioned in this paper, with a large number of applications to the moduli space construction problem, see, for instance, the work of Mumford and Fogarty.
Abstract: “Geometric Invariant Theory” by Mumford/Fogarty (the first edition was published in 1965, a second, enlarged edition appeared in 1982) is the standard reference on applications of invariant theory to the construction of moduli spaces. This third, revised edition has been long awaited for by the mathematical community. It is now appearing in a completely updated and enlarged version with an additional chapter on the moment map by Prof. Frances Kirwan (Oxford) and a fully updated bibliography of work in this area. The book deals firstly with actions of algebraic groups on algebraic varieties, separating orbits by invariants and construction quotient spaces; and secondly with applications of this theory to the construction of moduli spaces. It is a systematic exposition of the geometric aspects of the classical theory of polynomial invariants.
3,210 citations
Book•
1 Jan 1997TL;DR: In this paper, the Grauert-Mullich Theorem is used to define a moduli space for sheaves on K-3 surfaces, and the restriction of sheaves to curves is discussed.
Abstract: Preface to the second edition Preface to the first edition Introduction Part I. General Theory: 1. Preliminaries 2. Families of sheaves 3. The Grauert-Mullich Theorem 4. Moduli spaces Part II. Sheaves on Surfaces: 5. Construction methods 6. Moduli spaces on K3 surfaces 7. Restriction of sheaves to curves 8. Line bundles on the moduli space 9. Irreducibility and smoothness 10. Symplectic structures 11. Birational properties Glossary of notations References Index.
2,143 citations
TL;DR: In this article, the authors present a legal opinion on the applicability of commercial or impression systématiques in the context of the agreement of publication mathématique de l'I.H.S.
Abstract: © Publications mathématiques de l’I.H.É.S., 1994, tous droits réservés. L’accès aux archives de la revue « Publications mathématiques de l’I.H.É.S. » (http:// www.ihes.fr/IHES/Publications/Publications.html) implique l’accord avec les conditions générales d’utilisation (http://www.numdam.org/legal.php). Toute utilisation commerciale ou impression systématique est constitutive d’une infraction pénale. Toute copie ou impression de ce fichier doit contenir la présente mention de copyright.
1,277 citations
431 citations
TL;DR: In this article, a quasi-projective moduli functor for a polynomial h of degree n is presented, where the modulus functor is a coarse moduli scheme.
Abstract: Given a polynomial h of degree n let M h be the moduli functor of canonically polarized complex manifolds with Hilbert polynomial h. By [23] there exist a quasi-projective scheme M h together with a natural transformation
$$ \Psi :\mathcal{M}_h \to Hom(\_,M_h ) $$
such that M h is a coarse moduli scheme for M h . For a complex quasi-projective manifold U we will say that a morphism ϕ U → M h factors through the moduli stack, or that ϕ is induced by a family, if ϕ lies in the image of Ψ(U), hence if ϕ = Ψ(ƒ: V → U).
128 citations
Related Topics (5)
Performance Metrics
| Year | Papers |
|---|---|
| 2021 | 6 |
| 2020 | 4 |
| 2019 | 9 |
| 2018 | 4 |
| 2017 | 8 |
| 2016 | 5 |