Algebraic geometry: 1 Complex projective varieties
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin ; Heidelberg
Springer
1976
|
| Edition: | Corr. 2. print. |
| Series: | Grundlehren der mathematischen Wissenschaften
221 |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | X, 186 S. graph. Darst. |
| ISBN: | 3540076034 0387076034 |
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MARC
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Record in the Search Index
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| adam_text | Table of Contents
Introduction vii
Prerequisites ix
Chapter 1. Affine Varieties 1
§1A. Their Definition, Tangent Space, Dimension, Smooth and
Singular Points 1
§ IB. Analytic Uniformization at Smooth Points, Examples
of Topological Knottedness at Singular Points 9
§1C. 0x x a UFD when x Smooth; Divisor of Zeroes and Poles of
Functions 14
Chapter 2. Projective Varieties 20
§2A. Their Definition, Extension of Concepts from Affine to Projective
Case 20
§2B. Products, Segre Embedding, Correspondences 26
§2C. Elimination Theory, Noether s Normalization Lemma, Density
of Zariski Open Sets 33
Chapter 3. Structure of Correspondences 40
§3A. Local Properties—Smooth Maps, Fundamental Openness Principle,
Zariski s Main Theorem 40
§3B. Global Properties—Zariski s Connectedness Theorem,
Specialization Principle 49
§3C. Intersections on Smooth Varieties 56
Chapter 4. Chow s Theorem 59
§4A. Internally and Externally Defined Analytic Sets and their Local
Descriptions as Branched Coverings of C 59
§4B. Applications to Uniqueness of Algebraic Structure and
Connectedness 67
Chapter 5. Degree of a Projective Variety 70
§ 5A. Definition of deg X, mul^X, of the Blow up BX(X),
Effect of a Projection, Examples 70
vi Table of Contents
§5B. Bezout s Theorem 80
§ 5C. Volume of a Projective Variety; Review of Homology,
DeRham s Theorem, Varieties as Minimal Submanifolds 85
Chapter 6. Linear Systems 96
§ 6A. The Correspondence between Linear Systems and Rational Maps,
Examples; Complete Linear Systems are Finite Dimensional 96
§6B. Differential Forms, Canonical Divisors and Branch Loci 104
§6C. Hilbert Polynomials, Relations with Degree 110
Appendix to Chapter 6. The Weil Samuel Algebraic Theory of
Multiplicity 116
Chapter 7. Curves and Their Genus 127
§ 7A. Existence and Uniqueness of the Non Singular Model of Each
Function Field of Transcendence Degree 1 (after Albanese) 127
§ 7B. Arithmetic Genus = Topological Genus; Existence of Good
Projections to P1, P2, P3 131
§ 7C. Residues of Differentials on Curves, the Classical Riemann Roch
Theorem for Curves and Applications 142
§7D. Curves of Genus 1 as Plane Cubics and as Complex Tori C/L 149
Chapter 8. The Birational Geometry of Surfaces 156
§ 8A. Generalities on Blowing up Points 156
§ 8B. Resolution of Singularities of Curves on a Smooth Surface by
Blowing up the Surface; Examples 160
§ 8C. Factorization of Birational Maps between Smooth Surfaces;
the Trees of Infinitely Near Points 168
§ 8D. The Birational Map between P2 and the Quadric and Cubic
Surfaces; the 27 Lines on a Cubic Surface 172
Bibliography 181
List of Notations 183
Index 184
|
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| edition | Corr. 2. print. |
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| illustrated | Illustrated |
| indexdate | 2024-07-09T15:44:18Z |
| institution | BVB |
| isbn | 3540076034 0387076034 |
| language | English |
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| physical | X, 186 S. graph. Darst. |
| publishDate | 1976 |
| publishDateSearch | 1976 |
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| publisher | Springer |
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| series | Grundlehren der mathematischen Wissenschaften |
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| spelling | Mumford, David 1937- Verfasser (DE-588)115549021 aut Algebraic geometry 1 Complex projective varieties David Mumford Corr. 2. print. Berlin ; Heidelberg Springer 1976 X, 186 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Grundlehren der mathematischen Wissenschaften 221 Grundlehren der mathematischen Wissenschaften (DE-604)BV002361514 1 Grundlehren der mathematischen Wissenschaften 221 (DE-604)BV000000395 221 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=001541069&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mumford, David 1937- Algebraic geometry Grundlehren der mathematischen Wissenschaften |
| title | Algebraic geometry |
| title_auth | Algebraic geometry |
| title_exact_search | Algebraic geometry |
| title_full | Algebraic geometry 1 Complex projective varieties David Mumford |
| title_fullStr | Algebraic geometry 1 Complex projective varieties David Mumford |
| title_full_unstemmed | Algebraic geometry 1 Complex projective varieties David Mumford |
| title_short | Algebraic geometry |
| title_sort | algebraic geometry complex projective varieties |
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