منابع مشابه
Quotients by finite equivalence relations
Let f : X → Y be a finite morphism of schemes. Given Y , one can easily describe X by the coherent sheaf of algebras f∗OX . Here our main interest is the converse. Given X , what kind of data we need to construct Y ? For this question, the surjectivity of f is indispensable. The fiber product X ×Y X ⊂ X ×X defines an equivalence relation on X , and we expect to be able to reconstruct Y as the q...
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Given an action of an affine algebraic group with only trivial characters on a factorial variety, we ask for categorical quotients. We characterize existence in the category of algebraic varieties. Moreover, allowing constructible sets as quotients, we obtain a more general existence result, which, for example, settles the case of a finitely generated algebra of invariants. As an application, w...
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For a group G and N-series G of G let In R,G(G), n ≥ 0, denote the filtration of the group algebra R(G) induced by G , and IR(G) its augmentation ideal. For subgroups H of G , left ideals J of R(H) and right H -submodules M of IZZ(G) the quotients IR(G)J/MJ are studied by homological methods, notably for M = IZZ(G)IZZ(H), IZZ(H)IZZ(G) + IZZ([H,G])ZZ(G) and ZZ(G)IZZ(N) + In ZZ,G(G) with N CG whe...
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Geometric invariant theory (GIT) was developed in the 1960s by Mumford in order to construct quotients of reductive group actions on algebraic varieties and hence to construct and study a number of moduli spaces, including, for example, moduli spaces of bundles over a nonsingular projective curve [26, 28]. Moduli spaces often arise naturally as quotients of varieties by algebraic group actions,...
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This article is devoted to the problem of constructing geometric quotients of a quasiaffine scheme X over a field of characteristic 0 by a unipotent algebraic group G. This problem arises naturally if one tries to construct moduli spaces in the sense of Mumford's 'geometric invariant theory' for singularities of algebraic varieties or for modules over the local ring of such a singularity. Indee...
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ژورنال
عنوان ژورنال: Journal of the Australian Mathematical Society. Series A. Pure Mathematics and Statistics
سال: 1981
ISSN: 0263-6115
DOI: 10.1017/s1446788700017225