2012

A Royal Road to Algebraic Geometry

Authors:

ISBN: 978-3-642-19224-1 (Print) 978-3-642-19225-8 (Online)

Table of contents (22 chapters)

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  1. Front Matter

    Pages I-XIII

  2. Curves

    1. Front Matter

      Pages 1-1

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      Book Chapter

      Pages 3-12

      Affine and Projective Space

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      Book Chapter

      Pages 13-38

      Curves in \(\mathbb{A}^{2}_{k}\mbox{ and in }\mathbb{P}^{2}_{k}\)

    4. No Access

      Book Chapter

      Pages 39-62

      Higher Geometry in the Projective Plane

    5. No Access

      Book Chapter

      Pages 63-118

      Plane Curves and Algebra

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      Book Chapter

      Pages 119-139

      Projective Varieties in \(\mathbb{P}^{N}_{k}\)

  3. Introduction to Grothendieck's Theory of Schemes

    1. Front Matter

      Pages 141-141

    2. No Access

      Book Chapter

      Pages 143-160

      Categories and Functors

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      Book Chapter

      Pages 161-164

      Constructions and Representable Functors

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      Book Chapter

      Pages 165-183

      Abelian Categories

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      Book Chapter

      Pages 185-194

      The Concept of Spec(A)

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      Book Chapter

      Pages 195-215

      The Category of Schemes

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      Book Chapter

      Pages 217-238

      Properties of Morphisms of Schemes

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      Book Chapter

      Pages 239-245

      Modules, Algebras and Bundles on a Scheme

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      Book Chapter

      Pages 247-251

      More Properties of Morphisms, Scheme Theoretic Image and the “Sorite”

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      Book Chapter

      Pages 253-261

      Projective Schemes and Bundles

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      Book Chapter

      Pages 263-274

      Further Properties of Morphisms

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      Book Chapter

      Pages 275-284

      Conormal Sheaf and Projective Bundles

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      Book Chapter

      Pages 285-305

      Cohomology Theory on Schemes

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      Book Chapter

      Pages 307-319

      Intersection Theory

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      Book Chapter

      Pages 321-328

      Characteristic Classes in Algebraic Geometry

    16. No Access

      Book Chapter

      Pages 329-334

      The Riemann-Roch Theorem

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