Quasi-projective Moduli for Polarized Manifolds by Eckart Viehweg
Quasi-projective Moduli for Polarized Manifolds - Table of Contents
- 1. Moduli Problems and Hilbert Schemes and representable functors hilbert schemes universal families
- 2. Weakly Positive Sheaves and Vanishing Theorems and weak positivity kawamata viehweg vanishing theorem invertible sheaves
- 3. D. Mumford's Geometric Invariant Theory and mumford GIT stability stable semistable orbits quotient schemes
- 4. Stability and Ampleness Criteria and ample line bundles numerical stability criteria Hilbert points
- 5. Auxiliary Results on Locally Free Sheaves and Divisors and locally free sheaves reflexive sheaves divisor theory
- 6. Weak Positivity of Direct Images of Sheaves and direct image sheaves pushforward positivity kodaira dimension
- 7. Geometric Invariant Theory on Hilbert Schemes and GIT quotients hilbert points linearization action
- 8. Allowing Certain Singularities and canonical singularities log terminal singularities moduli compactification
- 9. Moduli as Algebraic Spaces and artin stack algebraic spaces coarse moduli spaces construction
What You Will Learn in Quasi-projective Moduli for Polarized Manifolds
In Quasi-projective Moduli for Polarized Manifolds (frequently studied alongside advanced treatises on moduli spaces and algebraic varieties), distinguished geometer Eckart Viehweg provides an authoritative, mathematically rigorous treatment of moduli construction. Unfolding across nine detailed chapters, this landmark work covers moduli problems, Hilbert schemes, weakly positive sheaves, vanishing theorems, David Mumford's Geometric Invariant Theory (GIT), stability and ampleness criteria, weak positivity of direct images, handling allowed singularities, and constructing moduli as algebraic spaces.
Targeted at doctoral students, algebraic geometers, and research mathematicians, Viehweg presents a deep, unified framework for constructing quasi-projective moduli spaces for higher-dimensional polarized manifolds. Readers are guided step-by-step through line bundle positivity, direct image sheaves, GIT quotient constructions, and birational classification techniques.
Renowned for its profound theoretical depth, structural clarity, and foundational influence on modern birational geometry, this volume stands as an indispensable reference for scholars seeking a definitive moduli spaces of algebraic varieties pdf for advanced study. It systematically equips quantitative researchers with powerful algebraic tools for mastering moduli theory and geometric invariant theory with confidence.
Book Details & Specifications
Title:
Quasi-projective Moduli for Polarized Manifolds by Eckart Viehweg
Publisher:
Springer
Year:
1995
Pages:
326
Type:
PDF
Language:
English
ISBN-10 #:
3642797474
ISBN-13 #:
978-3642797477
License:
Made available online with permission from Springer-Verlag
Amazon:
Amazon
About the Author: Eckart Viehweg
The author Eckart Viehweg
(1948–2010) was a world-renowned German algebraic geometer and Professor of Mathematics at the University of Duisburg-Essen.
Awarded the prestigious Leibniz Prize, Prof. Viehweg made groundbreaking contributions to classification theory and moduli of higher-dimensional algebraic varieties, authoring landmark research monographs that remain essential references for scholars seeking advanced moduli spaces of algebraic varieties pdf resources.
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