Author | Viehweg, Eckart. author |
---|---|
Title | Quasi-projective Moduli for Polarized Manifolds [electronic resource] / by Eckart Viehweg |
Imprint | Berlin, Heidelberg : Springer Berlin Heidelberg, 1995 |
Connect to | http://dx.doi.org/10.1007/978-3-642-79745-3 |
Descript | VIII, 320 p. online resource |
Leitfaden -- Classification Theory and Moduli Problems -- Notations and Conventions -- 1 Moduli Problems and Hilbert Schemes -- 1.1 Moduli Functors and Moduli Schemes -- 1.2 Moduli of Manifolds: The Main Results -- 1.3 Properties of Moduli Functors -- 1.4 Moduli Functors for ?-Gorenstein Schemes -- 1.5 A. Grothendieckโs Construction of Hilbert Schemes -- 1.6 Hilbert Schemes of Canonically Polarized Schemes -- 1.7 Hilbert Schemes of Polarized Schemes -- 2 Weakly Positive Sheaves and Vanishing Theorems -- 2.1 Coverings -- 2.2 Numerically Effective Sheaves -- 2.3 Weakly Positive Sheaves -- 2.4 Vanishing Theorems and Base Change -- 2.5 Examples of Weakly Positive Sheaves -- 3 D. Mumfordโs Geometric Invariant Theory -- 3.1 Group Actions and Quotients -- 3.2 Linearizations -- 3.3 Stable Points -- 3.4 Properties of Stable Points -- 3.5 Quotients, without Stability Criteria -- 4 Stability and Ampleness Criteria -- 4.1 Compactifications and the Hilbert-Mumford Criterion -- 4.2 Weak Positivity of Line Bundles and Stability -- 4.3 Weak Positivity of Vector Bundles and Stability -- 4.4 Ampleness Criteria -- 5 Auxiliary Results on Locally Free Sheaves and Divisors -- 5.1 O. Gabberโs Extension Theorem -- 5.2 The Construction of Coverings -- 5.3 Singularities of Divisors -- 5.4 Singularities of Divisors in Flat Families -- 5.5 Vanishing Theorems and Base Change, Revisited -- 6 Weak Positivity of Direct Images of Sheaves -- 6.1 Variation of Hodge Structures -- 6.2 Weakly Semistable Reduction -- 6.3 Applications of the Extension Theorem -- 6.4 Powers of Dualizing Sheaves -- 6.5 Polarizations, Twisted by Powers of Dualizing Sheaves -- 7 Geometric Invariant Theory on Hilbert Schemes -- 7.1 Group Actions on Hilbert Schemes -- 7.2 Geometric Quotients and Moduli Schemes -- 7.3 Methods to Construct Quasi-Projective Moduli Schemes -- 7.4 Conditions for the Existence of Moduli Schemes: Case (CP) -- 7.5 Conditions for the Existence of Moduli Schemes: Case (DP) -- 7.6 Numerical Equivalence -- 8 Allowing Certain Singularities -- 8.1 Canonical and Log-Terminal Singularities -- 8.2 Singularities of Divisors -- 8.3 Deformations of Canonical and Log-Terminal Singularities -- 8.4 Base Change and Positivity -- 8.5 Moduli of Canonically Polarized Varieties -- 8.6 Moduli of Polarized Varieties -- 8.7 Towards Moduli of Canonically Polarized Schemes -- 9 Moduli as Algebraic Spaces -- 9.1 Algebraic Spaces -- 9.2 Quotients by Equivalence Relations -- 9.3 Quotients in the Category of Algebraic Spaces -- 9.4 Construction of Algebraic Moduli Spaces -- 9.5 Ample Line Bundles on Algebraic Moduli Spaces -- 9.6 Proper Algebraic Moduli Spaces for Curves and Surfaces -- References -- Glossary of Notations