Titlebook: Quasi-projective Moduli for Polarized Manifolds; Eckart Viehweg Book 1995 Springer-Verlag Berlin Heidelberg 1995 Algebraische Räume.Birati

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Moduli Problems and Hilbert Schemes,erent moduli problems of manifolds. As a very first step towards their proofs, we will discuss properties a reasonable moduli functor should have and we will apply them to show that the manifolds or schemes considered correspond to the points of a locally closed subscheme of a certain Hilbert scheme.

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,D. Mumford’s Geometric Invariant Theory,he statements which are used in this monograph, except for those coming from the theory of algebraic groups, such as the finiteness of the algebra of invariants under the action of a reductive group, we include proofs. Usually we just reproduce the arguments given by Mumford in [59] (hopefully witho

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Allowing Certain Singularities,gularities or, being very optimistic, to certain reduced schemes. However, nothing is known about the local closedness and the boundedness of the corresponding moduli functors, as soon as the dimension of the objects is larger than two. Reducible or non-normal schemes have to be added to the objects

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Book 1995meters, which he proposes to name "moduli". A precise formulation of global moduli problems in algebraic geometry, the definition of moduli schemes or of algebraic moduli spaces for curves and for certain higher dimensional manifolds have only been given recently (A. Grothendieck, D. Mumford, see [5

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