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Quasi-projective Moduli for Polarized Manifolds

  • Eckart Viehweg

Part of the Ergebnisse der Mathematik und ihrer Grenzgebiete book series (MATHE3, volume 30)

Table of contents

  1. Front Matter
    Pages I-VIII
  2. Eckart Viehweg
    Pages 1-14
  3. Eckart Viehweg
    Pages 15-52
  4. Eckart Viehweg
    Pages 77-110
  5. Eckart Viehweg
    Pages 111-138
  6. Eckart Viehweg
    Pages 167-196
  7. Eckart Viehweg
    Pages 197-238
  8. Eckart Viehweg
    Pages 239-276
  9. Eckart Viehweg
    Pages 277-310
  10. Back Matter
    Pages 311-320

About this book

Introduction

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.

Keywords

Algebraische Räume Birationale Geometrie Divisor Geometrische Invarianten-Theorie Grothendieck topology Moduli Schemata Moduli schemes Polarisierte Mannigfaltigkeiten Schema algebraic geometry algebraic spaces birational geometry geometric invariant theory manifold polarized manifolds

Authors and affiliations

  • Eckart Viehweg
    • 1
  1. 1.Fachbereich 6, MathematikUniversität-Gesamthochschule EssenEssenGermany

Bibliographic information

  • DOI https://doi.org/10.1007/978-3-642-79745-3
  • Copyright Information Springer-Verlag Berlin Heidelberg 1995
  • Publisher Name Springer, Berlin, Heidelberg
  • eBook Packages Springer Book Archive
  • Print ISBN 978-3-642-79747-7
  • Online ISBN 978-3-642-79745-3
  • Series Print ISSN 0071-1136
  • Buy this book on publisher's site