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Algemene relativiteitstheorie --- General relativity (Physics) --- Manifolds (Mathematics) --- Menigvuldigheden (Wiskunde) --- Relativiteit [Algemene ] (Fysica) --- Relativiteitstheorie [Algemene ] --- Relativité générale (Physique) --- Varietes (Mathematiques)

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The concept of moduli goes back to B. Riemann, who shows in [68] that the isomorphism class of a Riemann surface of genus 9 ~ 2 depends on 3g - 3 parameters, 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 [59]), as well as solutions in some cases. It is the aim of this monograph to present methods which allow over a field of characteristic zero to construct certain moduli schemes together with an ample sheaf. Our main source of inspiration is D. Mumford's "Geometric In­ variant Theory". We will recall the necessary tools from his book [59] and prove the "Hilbert-Mumford Criterion" and some modified version for the stability of points under group actions. As in [78], a careful study of positivity proper­ ties of direct image sheaves allows to use this criterion to construct moduli as quasi-projective schemes for canonically polarized manifolds and for polarized manifolds with a semi-ample canonical sheaf.

Manifolds (Mathematics) --- Menigvuldigheden (Wiskunde) --- Modules [Projective ] (Algebra) --- Projective modules (Algebra) --- Varietes (Mathematiques) --- Moduli theory. --- Manifolds (Mathematics). --- Geometry, algebraic. --- Differential equations, partial. --- Algebraic Geometry. --- Several Complex Variables and Analytic Spaces. --- Algebraic geometry. --- Functions of complex variables.

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Foliations is one of the major concepts of modern geometry and topology meaning a partition of topological space into a disjoint sum of leaves. This book is devoted to geometry and topology of surface foliations and their links to ergodic theory, dynamical systems, complex analysis, differential and noncommutative geometry. This comprehensive book addresses graduate students and researchers and will serve as a reference book for experts in the field.

Differential geometry. Global analysis --- Menigvuldigheden (Wiskunde) --- Varietes (Mathematiques) --- Foliations (Mathematics) --- Manifolds (Mathematics). --- Complex manifolds. --- Global analysis (Mathematics). --- Combinatorics. --- Manifolds and Cell Complexes (incl. Diff.Topology). --- Global Analysis and Analysis on Manifolds. --- Combinatorics --- Algebra --- Mathematical analysis --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- Analytic spaces --- Manifolds (Mathematics) --- Geometry, Differential --- Topology

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514.84 --- Global analysis (Mathematics) --- Manifolds (Mathematics) --- 514.74 --- 514.74 Algebraic and analytic methods in geometry --- Algebraic and analytic methods in geometry --- Geometry, Differential --- Topology --- Analysis, Global (Mathematics) --- Differential topology --- Functions of complex variables --- Geometry, Algebraic --- 514.84 Geometric methods in quantum mechanics and in the theory of elementary particles --- Geometric methods in quantum mechanics and in the theory of elementary particles --- Analyse globale (Mathematiques) --- Globale analyse (Wiskunde) --- Menigvuldigheden (Wiskunde) --- Varietes (Mathematiques)