Eckart Viehweg

(Author)

Quasi-Projective Moduli for Polarized Manifolds (Softcover Reprint of the Original 1st 1995)Paperback - Softcover Reprint of the Original 1st 1995, 27 December 2011

Quasi-Projective Moduli for Polarized Manifolds (Softcover Reprint of the Original 1st 1995)
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Part of Series
Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge /
Part of Series
Ergebnisse Der Mathematik Und Ihrer Grenzgebiete. 3. Folge a
Print Length
320 pages
Language
English
Publisher
Springer
Date Published
27 Dec 2011
ISBN-10
3642797474
ISBN-13
9783642797477

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.

Product Details

Author:
Eckart Viehweg
Book Edition:
Softcover Reprint of the Original 1st 1995
Book Format:
Paperback
Country of Origin:
NL
Date Published:
27 December 2011
Dimensions:
23.39 x 15.6 x 1.75 cm
ISBN-10:
3642797474
ISBN-13:
9783642797477
Language:
English
Location:
Berlin, Heidelberg
Pages:
320
Publisher:
Weight:
467.2 gm

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