Details

Autor(en) / Beteiligte

• Lamotke, Klaus

Titel

Regular Solids and Isolated Singularities [electronic resource]

Auflage

1st ed. 1986

Ort / Verlag

Wiesbaden : Vieweg+Teubner Verlag

Erscheinungsjahr

1986

Link zum Volltext

• SpringerLink Books - AutoHoldings

Beschreibungen/Notizen

• I: Regular Solids and Finite Rotation Groups -- §1. The Platonic Solids -- §2. Convex Polytopes -- §3. Regular Solids -- §4. Enumeration and Realization of Regular Solids -- §5. The Rotation Groups of the Platonic Solids -- §6. Finite Subgroups of the Rotation Group SO(3) -- §7. Normal Subgroups -- §8. Generators and Relations for the Finite Subgroups of SO(3) -- II: Finite Subgroups of SL(2,G) and Invariant Polynomials -- §1. Finite Subgroups of SL(2,C) -- §2. Quaternions and Rotations -- §3. Four-Dimensional Regular Solids -- §4. The Orbit Spaces S3/G of the Finite Subgroups G of SU(2) -- §5. Generators and Relations for the Finite Subgroups of SL(2,C) -- §6. Invariant Divisors and Semi-Invariant Forms -- §7. The Characters of the Invariant Divisors -- §8. Generators and Relations for the Algebra of Invariant Polynomials -- §9. The Affine Orbit Variety -- III: Local Theory of Several Complex Variables -- §1. Germs of Holomorphic Functions -- §2. Germs of Analytic Sets -- §3. Germs of Holomorphic Maps -- §4. The Embedding Dimension -- §5. The Preparation Theorem -- §6. Finite Maps -- §7. Finite and Strict Maps -- §8. The Nullstellensatz -- §9. The Dimension -- §10. Annihilators -- §11. Regular Sequences -- §12. Complete Intersections -- §13. Complex Spaces -- IV: Quotient Singularities and Their Resolutions -- §1. Germs of Invariant Holomorphic Functions -- §2. Complex Orbit Spaces -- §3. Quotient Singularities -- §4. Modifications. Line Bundles -- §5. Cyclic Quotient Singularities -- §6. The Resolution of Cyclic Quotient Singularities -- §7. The Cotangent Action -- §8. Line Bundles with Singularities -- §9. The Resolution of Non-Cyclic Quotient Singularities -- §10. Plumbed Surfaces -- §11. Intersection Numbers -- §12. The Homology of Plumbed Surfaces -- §13. The Fundamental Group of a Plumbed Surface Minus its Core -- §14. Groups Determined by a Weighted Tree -- §15. Topological Invariants -- V: The Hierarchy of Simple Singularities -- §1. Basic Concepts -- §2. The Milnor Number -- §3. Transformation Groups -- §4. Families of Germs -- §5. Finitely Determined Germs -- §6. Unfoldings -- §7. The Multiplicity -- §8. Weighted Homogeneous Polynomials -- §9. The Classification of Holomorphic Germs -- §10. Three Series of Holomorphic Germs -- §11. Simple Singularities -- §12. Adjacency -- §13. Conclusion and Outlook -- References.