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2012

A Royal Road to Algebraic Geometry

Authors:

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

Table of contents (22 chapters)

Front Matter

Pages I-XIII

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Curves
1. Front Matter
  
  Pages 1-1
  
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2. Book Chapter
  
  Pages 3-12
  
  Affine and Projective Space
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3. Book Chapter
  
  Pages 13-38
  
  Curves in $\mathbb{A}^{2}_{k}\mbox{ and in }\mathbb{P}^{2}_{k}$
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4. Book Chapter
  
  Pages 39-62
  
  Higher Geometry in the Projective Plane
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5. Book Chapter
  
  Pages 63-118
  
  Plane Curves and Algebra
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6. Book Chapter
  
  Pages 119-139
  
  Projective Varieties in $\mathbb{P}^{N}_{k}$
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Introduction to Grothendieck's Theory of Schemes
1. Front Matter
  
  Pages 141-141
  
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2. Book Chapter
  
  Pages 143-160
  
  Categories and Functors
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3. Book Chapter
  
  Pages 161-164
  
  Constructions and Representable Functors
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4. Book Chapter
  
  Pages 165-183
  
  Abelian Categories
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5. Book Chapter
  
  Pages 185-194
  
  The Concept of Spec(A)
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6. Book Chapter
  
  Pages 195-215
  
  The Category of Schemes
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7. Book Chapter
  
  Pages 217-238
  
  Properties of Morphisms of Schemes
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8. Book Chapter
  
  Pages 239-245
  
  Modules, Algebras and Bundles on a Scheme
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9. Book Chapter
  
  Pages 247-251
  
  More Properties of Morphisms, Scheme Theoretic Image and the “Sorite”
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10. Book Chapter
  
  Pages 253-261
  
  Projective Schemes and Bundles
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11. Book Chapter
  
  Pages 263-274
  
  Further Properties of Morphisms
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12. Book Chapter
  
  Pages 275-284
  
  Conormal Sheaf and Projective Bundles
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13. Book Chapter
  
  Pages 285-305
  
  Cohomology Theory on Schemes
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14. Book Chapter
  
  Pages 307-319
  
  Intersection Theory
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15. Book Chapter
  
  Pages 321-328
  
  Characteristic Classes in Algebraic Geometry
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16. Book Chapter
  
  Pages 329-334
  
  The Riemann-Roch Theorem
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