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Quasi-projective Moduli for Polarized Manifolds by Eckart Viehweg
Quasi-projective Moduli for Polarized Manifolds by Eckart Viehweg
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Quasi-projective Moduli for Polarized Manifolds

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Description

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.
Release date Australia
December 27th, 2011
Audience
  • Professional & Vocational
Edition
Softcover reprint of the original 1st ed. 1995
Illustrations
viii, 320 p.
Pages
320
Dimensions
156x234x17
ISBN-13
9783642797477
Product ID
20764348

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