Algebraic Geometry

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Springer Science & Business Media, 29.06.2013 - 496 Seiten
Robin Hartshorne studied algebraic geometry with Oscar Zariski and David Mumford at Harvard, and with J.-P. Serre and A. Grothendieck in Paris. After receiving his Ph.D. from Princeton in 1963, Hartshorne became a Junior Fellow at Harvard, then taught there for several years. In 1972 he moved to California where he is now Professor at the University of California at Berkeley. He is the author of "Residues and Duality" (1966), "Foundations of Projective Geometry (1968), "Ample Subvarieties of Algebraic Varieties" (1970), and numerous research titles. His current research interest is the geometry of projective varieties and vector bundles. He has been a visiting professor at the College de France and at Kyoto University, where he gave lectures in French and in Japanese, respectively. Professor Hartshorne is married to Edie Churchill, educator and psychotherapist, and has two sons. He has travelled widely, speaks several foreign languages, and is an experienced mountain climber. He is also an accomplished amateur musician: he has played the flute for many years, and during his last visit to Kyoto he began studying the shakuhachi.
 

Inhalt

Morphisms
14
Nonsingular Varieties
31
Intersections in Projective Space
47
CHAPTER II
60
First Properties of Schemes
82
Separated and Proper Morphisms
95
Sheaves of Modules
108
Divisors
129
The Canonical Embedding
340
Classification of Curves in P
349
CHAPTER V
356
Geometry on a Surface
357
Ruled Surfaces
369
Monoidal Transformations
386
The Cubic Surface in P3
395
Birational Transformations
409

Projective Morphisms
149
Differentials
172
Formal Schemes
190
Cohomology of Sheaves
206
Cech Cohomology
219
The Cohomology of Projective Space
225
Ext Groups and Sheaves
233
The Serre Duality Theorem
239
Higher Direct Images of Sheaves
250
Flat Morphisms
253
Smooth Morphisms
268
The Theorem on Formal Functions
276
The Semicontinuity Theorem
281
CHAPTER IV
293
RiemannRoch Theorem
294
Hurwitzs Theorem
299
Embeddings in Projective Space
307
Elliptic Curves
316
Classification of Surfaces
421
APPENDIX A Intersection Theory
424
Intersection Theory
425
Properties of the Chow Ring
428
Chern Classes
429
The RiemannRoch Theorem
431
Complements and Generalizations
434
APPENDIX B Transcendental Methods
438
Comparison of the Algebraic and Analytic Categories
440
When is a Compact Complex Manifold Algebraic?
441
Kähler Manifolds
445
The Exponential Sequence
446
APPENDIX C
449
Bibliography
459
Results from Algebra
470
Index
478
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