Local Analytic Geometry
Local Analytic Geometry
Published on 1. January 1964
483 pages
978-0-08-087326-8 (ISBN)
Description
Local Analytic Geometry
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Content
- Front Cover
- Local Analytic Geometry
- Copyright Page
- Contents
- Preface
- Instructions to the Reader
- Chapter I. Elementary Theory in Cn
- 1. Notation and Terminology
- 2. Convergent Power Series
- 3. Laurent Series
- 4. Cauchy Theory
- 5. Convexity in Rn
- 6. Laurent Expansion in Cn
- 7. Domains of Holomorphy
- 8. A Theorem of Rad?
- 9. Comments on Totally Disconnected Fields
- Chapter II. Weierstrass Preparation Theorem
- 10. Weierstrass Preparation Theorem. Identity Theorem. Finite Ideal Bases and Unique Factorization in Power Series Rings. Implicit Function Theorem
- 11. Continuity of Roots and Open Map Theorem
- 12. Hensel's Lemma. Continuity of Algebroid Functions
- 13. Complex Weierstrass Preparation Theorem
- 14. Riemann Extension Theorem and Connectivity of Algebroid Hypersurfaces
- 15. Oka Coherence
- 16. Cartan Module Bases
- Chapter III. Review from Local Algebra
- 17. Depth, Height, and Dimension. Completions. Direct Sums. Resultants and Discriminants
- 18. Quotient Rings
- 19. Integral Dependence and Finite Generation
- 20. Henselian Rings
- 21. Order and Rank in Local Rings. Regular Local Rings
- 22. Another Proof that a Formal Power Series Rings is Noetherian
- Chapter IV. Parameters in Power Series Rings
- 23. Parameters for Ideals
- 24. Perfect Fields
- 25. Regularity of Quotient Rings
- 26. Translates of Ideals
- 27. Dimension of an Intersection
- 28. Algebraic Lemmas on Algebroid Functions
- Chapter V. Analytic Sets
- 29. The Language of Germs
- 30. Decomposition of an Analytic Set Germ
- 31. Rückert-Weierstrass Parametrization of an Irreducible Analytic Set Germ
- 32. Rückert-Weierstrass Parametrization of an Irreducible Analytic Set Germ (Summary)
- 33. Local Properties of Analytic Sets
- 34. Connectivity Properties of Complex Analytic Sets
- 35. Parametrization of a Pure Dimensional Analytic Set
- 36. Normal Points of Complex Analytic Sets. Remarks on Algebraic Varieties
- 37. Remmert-Stein-Thullen Theorem on Essential Singularities of Complex Analytic Sets. Theorem of Chow
- 38. Topological Dimension
- 39. Remarks on the Fundamental Group
- Chapter VI. Language of Sheaves
- 40. Inductive Systems and Presheaves
- 41. Sheaves
- 42. Coherent Sheaves
- Chapter VII. Analytic Spaces
- 43. Definitions
- 44. Recapitulation of Properties of Analytic Spaces
- 45. Invariance of Order and Rank
- 46. Bimeromorphic Maps and Normalizations
- Bibliography
- Index of Notation
- Subject Index
