A Royal Road to Algebraic Geometry

Table of Contents

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   Book Overview
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   Chapter 1 Affine and Projective Space
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   Chapter 2 Curves in $\mathbb{A}^{2}_{k}\mbox{ and in }\mathbb{P}^{2}_{k}$
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   Chapter 3 Higher Geometry in the Projective Plane
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   Chapter 4 Plane Curves and Algebra
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   Chapter 5 Projective Varieties in $\mathbb{P}^{N}_{k}$
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   Chapter 6 Categories and Functors
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   Chapter 7 Constructions and Representable Functors
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   Chapter 8 Abelian Categories
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    Chapter 9 The Concept of Spec(A)
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    Chapter 10 The Category of Schemes
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    Chapter 11 Properties of Morphisms of Schemes
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    Chapter 12 Modules, Algebras and Bundles on a Scheme
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    Chapter 13 More Properties of Morphisms, Scheme Theoretic Image and the “Sorite”
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    Chapter 14 Projective Schemes and Bundles
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    Chapter 15 Further Properties of Morphisms
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    Chapter 16 Conormal Sheaf and Projective Bundles
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    Chapter 17 Cohomology Theory on Schemes
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    Chapter 18 Intersection Theory
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    Chapter 19 Characteristic Classes in Algebraic Geometry
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    Chapter 20 The Riemann-Roch Theorem
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    Chapter 21 Some Basic Constructions in the Category of Projective k -Varieties
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    Chapter 22 More on Duality