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Review: Algebraic GeometryUser Review - Joecolelife - Goodreads
Robin Hartshorne is a master of Grothendieck's general machinery for generalizing the tools of classical algebraic geometry to apply to families of varieties, and more broadly to number theory. A ... Read full review
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Review: Algebraic GeometryUser Review - James Swenson - Goodreads
Where's the geometry? It would be far too easy to spend a year reading this book and end up knowing that the Krull dimension of the ring k[x,y] is two, but unable to explain why this indicates that ... Read full review
1-module 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 quasi-coherent quasi-coherent sheaf quotient rational regular functions Riemann-Roch ringed space ruled surface sheaf of ideals sheaves singular Spec surjective tangent theorem topological space unique valuation ring Zariski
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