Principles of algebraic geometry:
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Wiley
1994
|
| Schriftenreihe: | Wiley classics library
A Wiley interscience publication |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XII, 813 S. graph. Darst. |
| ISBN: | 0471050598 9780471050599 |
Internformat
MARC
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| 100 | 1 | |a Griffiths, Phillip |d 1938- |e Verfasser |0 (DE-588)131881434 |4 aut | |
| 245 | 1 | 0 | |a Principles of algebraic geometry |c Phillip Griffiths and Joseph Harris |
| 264 | 1 | |a New York [u.a.] |b Wiley |c 1994 | |
| 300 | |a XII, 813 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
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| 700 | 1 | |a Harris, Joseph |e Verfasser |4 aut | |
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| 999 | |a oai:aleph.bib-bvb.de:BVB01-006788602 | ||
Datensatz im Suchindex
| _version_ | 1804124623788310528 |
|---|---|
| adam_text | CONTENTS
CHAPTER
0
FOUNDATIONAL MATERIAL
1
1.
Rudiments of Several Complex Variables
Cauchy s Formula and Applications
2
Several Variables
6
Weierstrass
Theorems and Corollaries
7
Analytic Varieties
12
2.
Complex Manifolds
Complex Manifolds
14
Submanifolds and Subvarieties
18
De Rham
and Dolbeault Cohomology
23
Calculus on Complex Manifolds
27
3.
Sheaves and Cohomology
Origins: The Mittag-Leffler Problem
34
Sheaves
35
Cohomology of Sheaves
38
The
de Rham
Theorem
43
The Dolbeault Theorem
45
4.
Topology of Manifolds
Intersection of Cycles
49
Poincaré
Duality
53
Intersection of Analytic Cycles
60
5.
Vector Bundles, Connections, and Curvature
Complex and Holomorphic Vector Bundles
66
Metrics, Connections, and Curvature
71
6.
Harmonic Theory on Compact Complex Manifolds
The Hodge Theorem
80
Proof of the Hodge Theorem I: Local Theory
84
vii
ущ
CONTENTS
Proof of the Hodge Theorem II: Global Theory
92
Applications of the Hodge Theorem
100
7. Kahler
Manifolds
The
Kahler
Condition 106
The Hodge Identities and the Hodge Decomposition
111
The
Lef
schetz Decomposition
118
CHAPTER
1
COMPLEX ALGEBRAIC VARIETIES
128
1.
Divisors and Line Bundles
Divisors
129
Line Bundles I32
Chera
Classes of Line Bundles
139
2.
Some Vanishing Theorems and Corollaries
The Kodaira Vanishing Theorem
148
The
Lef
schetz Theorem on
Hyperplane
Sections
156
Theorem
В І59
The Lefschetz Theorem on
(1,
l)-classes
161
3.
Algebraic Varieties
Analytic and Algebraic Varieties
164
Degree of a Variety
»71
Tangent Spaces to Algebraic Varieties
175
4.
The Kodaira Embedding Theorem
Line Bundles and Maps to
Projective
Space
176
Blowing Up
182
Proof of the Kodaira Theorem
189
5.
Grassmannians
Definitions
193
The Cell Decomposition
194
The Schubert Calculus
197
Universal Bundles
207
The Pliicker Embedding
209
CHAPTER
2
RIEMANN SURFACES AND ALGEBRAIC
CURVES
212
1.
Preliminaries
Embedding Riemann Surfaces
213
The Riemann-Hurwitz Formula
216
CONTENTS ix
The Genus
Formula
219
Cases g
=0,1 222
2.
Abel s Theorem
Abel s Theorem
—
First Version
224
The First Reciprocity Law and Corollaries
229
Abel s Theorem
—
Second Version
232
Jacobi Inversion
235
3.
Linear Systems on Curves
Reciprocity Law II
240
The Riemann-Roch Formula
243
Canonical Curves
246
Special Linear Systems I
249
Hyperelliptic Curves and Riemann s Count
253
Special Linear Systems II
259
4.
Pliicker Formulas
Associated Curves
263
Ramification
264
The General
Plücker
Formulas I
268
The General
Plücker
Formulas II
271
Weierstrass
Points
273
Plücker
Formulas for Plane Curves
277
5.
Correspondences
Definitions and Formulas
282
Geometry of Space Curves
290
Special Linear Systems III
298
6.
Complex Tori and Abelian Varieties
The Riemann Conditions
300
Line Bundles on Complex Tori
307
Theta-Functions
317
The Group Structure on an Abelian Variety
324
Intrinsic Formulations
326
7.
Curves and Their Jacobians
Preliminaries
333
Riemann s Theorem
338
Riemann s Singularity Theorem
341
Special Linear Systems IV
349
Torelli s Theorem
359
x
CONTENTS
CHAPTER
3
FURTHER TECHNIQUES
364
1.
Distributions and Currents
Definitions; Residue Formulas
366
Smoothing and Regularity
373
Cohomology of Currents
382
2.
Applications of Currents to Complex Analysis
Currents Associated to Analytic Varieties
385
Intersection Numbers of Analytic Varieties
392
The
Levi
Extension and Proper Mapping Theorems
395
3.
Chern Classes
Definitions
400
The Gauss Bonnet Formulas
409
Some Remarks
—
Not Indispensable
—
Concerning
Chern Classes of Holomorphic Vector Bundles
416
4.
Fixed-Point and Residue Formulas
The Lefschetz Fixed-Point Formula
419
The Holomorphic Lefschetz Fixed-Point Formula
422
The
Bott
Residue Formula
426
The General Hirzebruch-Riemann-Roch Formula
435
5.
Spectral Sequences and Applications
Spectral Sequences of Filtered and Bigraded Complexes
438
Hypercohomology
445
Differentials of the Second Kind
454
The Leray Spectral Sequence
462
CHAPTER
4
SURFACES
469
1.
Preliminaries
Intersection Numbers, the Adjunction Formula,
and Riemann-Roch
470
Blowing Up and Down
473
The Quadric Surface
478
The Cubic Surface
480
2.
Rational Maps
Rational and
Birational
Maps
489
Curves on an Algebraic Surface
498
The Structure of
Birational
Maps Between Surfaces
510
3.
Rational Surfaces I
Noether s Lemma
513
Rational Ruled Surfaces
514
CONTENTS xi
The General Rational
Surface
520
Surfaces of Minimal Degree
522
Curves of Maximal Genus
527
Steiner
Constructions
528
The Enriques-Petri Theorem
533
4.
Rational Surfaces II
The Castelnuovo-Enriques Theorem
536
The
Enriques
Surface
541
Cubic Surfaces Revisited
545
The Intersection of Two Quadrics in P4
550
5.
Some Irrational Surfaces
The
Albanese
Map
552
Irrational Ruled Surfaces
553
A Brief Introduction to Elliptic Surfaces
564
Kodaira Number and the Classification Theorem I
572
The Classification Theorem II
582
K-3 Surfaces
590
Enriques
Surfaces
594
6.
Noether s Formula
Noether s Formula for Smooth Hypersurfaces
600
Blowing Up Submanifolds
602
Ordinary Singularities of Surfaces
611
Noether s Formula for General Surfaces
618
Some Examples
628
Isolated Singularities of Surfaces
636
CHAPTER
5
RESIDUES
647
1.
Elementary Properties of Residues
Definition and Cohomological Interpretation
649
The Global Residue Theorem
655
The Transformation Law and Local Duality
656
2.
Applications of Residues
Intersection Numbers
662
Finite Holomorphic Mappings
667
Applications to Plane
Projective
Geometry
670
3.
Rudiments of Commutative and Homological Algebra
with Applications
Commutative Algebra
678
Homological Algebra
682
The
Koszul
Complex and Applications
687
A Brief Tour Through Coherent Sheaves
695
xli
CONTENTS
4.
Global Duality
Global Ext
705
Explanation of the General Global Duality Theorem
707
Global Ext and Vector Fields with Isolated Zeros
708
Global Duality and Superabundance of
Points on a Surface
712
Extensions of Modules
722
Points on a Surface and Rank-Two Vector Bundles
726
Residues and Vector Bundles
729
CHAPTER
б
THE QUADRIC LINE COMPLEX
733
1.
Preliminaries: Quadrics
Rank of a Quadric
734
Linear Spaces on Quadrics
735
Linear Systems of Quadrics
741
Lines on Linear Systems of Quadrics
746
The Problem of Five Conies
749
2.
The Quadric Line Complex: Introduction
Geometry of the Grassmannian G(2,4)
756
Line Complexes
759
The Quadric Line Complex and Associated
Kummer
Surface I
762
Singular Lines of the Quadric Line Complex
767
Two Configurations
773
3.
Lines on the Quadric Line Complex
The Variety of Lines on the Quadric Line Complex
778
Curves on the Variety of Lines
780
Two Configurations Revisited
784
The Group Law
787
4.
The Quadric Line Complex: Reprise
The Quadric Line Complex and Associated
Kummer
Surface II
791
Rationality of the Quadric Line Complex
796
INDEX
805
|
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| id | DE-604.BV010215674 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T17:48:37Z |
| institution | BVB |
| isbn | 0471050598 9780471050599 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-006788602 |
| oclc_num | 473573723 |
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| physical | XII, 813 S. graph. Darst. |
| publishDate | 1994 |
| publishDateSearch | 1994 |
| publishDateSort | 1994 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley classics library A Wiley interscience publication |
| spelling | Griffiths, Phillip 1938- Verfasser (DE-588)131881434 aut Principles of algebraic geometry Phillip Griffiths and Joseph Harris New York [u.a.] Wiley 1994 XII, 813 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley classics library A Wiley interscience publication Algebraische Geometrie (DE-588)4001161-6 gnd rswk-swf Algebraische Geometrie (DE-588)4001161-6 s DE-604 Harris, Joseph Verfasser aut Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006788602&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Griffiths, Phillip 1938- Harris, Joseph Principles of algebraic geometry Algebraische Geometrie (DE-588)4001161-6 gnd |
| subject_GND | (DE-588)4001161-6 |
| title | Principles of algebraic geometry |
| title_auth | Principles of algebraic geometry |
| title_exact_search | Principles of algebraic geometry |
| title_full | Principles of algebraic geometry Phillip Griffiths and Joseph Harris |
| title_fullStr | Principles of algebraic geometry Phillip Griffiths and Joseph Harris |
| title_full_unstemmed | Principles of algebraic geometry Phillip Griffiths and Joseph Harris |
| title_short | Principles of algebraic geometry |
| title_sort | principles of algebraic geometry |
| topic | Algebraische Geometrie (DE-588)4001161-6 gnd |
| topic_facet | Algebraische Geometrie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=006788602&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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