Algebraic GeometryRobin 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. |
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User Review - bluelephant - LibraryThingI struggled through its first three chapters during two grad courses at UIUC. I didn't quite understand what I was doing at the very end but I found the whole thing enjoyable and sometimes even fun ... Read full review
Contents
Cohomology of Sheaves | 206 |
CHAPTER IV | 293 |
CHAPTER V | 356 |
APPENDIX | 424 |
APPENDIX B | 438 |
APPENDIX C | 449 |
Bibliography | 459 |
Results from Algebra | 470 |
Divisors | 129 |
Projective Morphisms | 149 |
Differentials | 172 |
Formal Schemes | 190 |
Index | 478 |
438 | 481 |
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Common terms and phrases
0x-modules abelian groups affine scheme affine variety algebraic set algebraically closed field ample automorphism birational Cartier divisor closed immersion closed point closed subscheme closed subset codimension coherent sheaf cohomology corresponding curve of degree define definition denote dimension elements elliptic curve embedding equivalent exact sequence Example fibre finite morphism finite number finite type follows function field functor Furthermore gives global sections graded ring Grothendieck Hence homomorphism hyperplane hypersurface induced injective integral invertible sheaf isomorphism Lemma Let f linear system locally free sheaf maximal ideal module morphism f multiplicity natural map noetherian ring noetherian scheme nonsingular curve nonsingular projective nonsingular variety open affine subset open set open subset phism polynomial presheaf prime ideal Proj projective space projective variety PROOF Proposition quasi-coherent sheaf quotient regular functions Riemann–Roch ruled surface sheaf of ideals sheaves singular Spec subvariety surjective tangent theorem topological space unique Zariski zero


