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
Review: Algebraic Geometry
User Review  Geoffrey Lee  GoodreadsI had great trouble with chapter two of this book. Some of my confusion has been mitigated after finding Eisenbud's book The Geometry of Schemes, but I am still trying to familiarize myself with the ... Read full review
Contents
II  1 
III  8 
IV  14 
V  24 
VI  31 
VII  39 
VIII  47 
IX  55 
XXXIV  299 
XXXV  307 
XXXVI  316 
XXXVII  340 
XXXVIII  349 
XXXIX  356 
XL  357 
XLI  369 
X  60 
XI  69 
XII  82 
XIII  95 
XIV  108 
XV  129 
XVI  149 
XVII  172 
XVIII  190 
XIX  201 
XX  202 
XXI  206 
XXII  213 
XXIII  218 
XXIV  225 
XXV  233 
XXVI  239 
XXVII  250 
XXVIII  253 
XXIX  268 
XXX  276 
XXXI  281 
XXXII  293 
XXXIII  294 
Common terms and phrases
1module abelian groups algebraically closed field automorphism base points birational Cartier divisor closed immersion closed point closed subscheme closed subset coherent sheaf cohomology corresponding curve of degree curve of genus define definition denote dimension elements elliptic curve embedding exact sequence Example fibre finite morphism finite type flasque flat follows function field functor genus g gives global sections Grothendieck Hence homogeneous homomorphism induced injective integral invertible sheaf isomorphism Lemma linear system linearly equivalent locally free sheaf maximal ideal module monoidal transformation morphism f:X multiplicity natural map noetherian ring noetherian scheme nonsingular curve nonsingular projective nonsingular variety open affine subset open set open subset plane polynomial prime ideal Proj projective space projective variety PROOF Proposition quasicoherent quasicoherent sheaf quotient rational regular functions RiemannRoch ringed space ruled surface sheaf of ideals sheaves singular Spec surjective tangent theorem topological space unique valuation ring Zariski
Popular passages
Page 469  A simple analytical proof of a fundamental property of birational transformations', Proc.