A Royal Road to Algebraic Geometry

• Main Author: Holme, Audun (Author)
• Corporate Author: SpringerLink (Online service)
• Format: Electronic eBook
• Language: English
• Published: Berlin, Heidelberg : Springer Berlin Heidelberg, 2012.
• Subjects: Mathematics.; Algebraic geometry.; Category theory (Mathematics).; Homological algebra.; Commutative algebra.; Commutative rings.; Geometry.; History.; Algebraic topology.; Algebraic Geometry.; Category Theory, Homological Algebra.; Algebraic Topology.; Commutative Rings and Algebras.; History of Mathematical Sciences.

This book is about modern algebraic geometry. The title A Royal Road to Algebraic Geometry is inspired by the famous anecdote about the king asking Euclid if there really existed no simpler way for learning geometry, than to read all of his work Elements. Euclid is said to have answered: “There is n...

Table of Contents:

• Part I Curves: 1 Affine and Projective Space
• 2 Curves in A2 k and in P2
• 3 Higher Geometry in the Projective Plane
• 4 Plane Curves and Algebra
• 5 Projective Varieties in PNk
• Part II Introduction to Grothendieck’s Theory of Schemes: 6 Categories and Functors
• 7 Constructions and Representable Functors
• 8 Abelian Categories
• 9 The Concept of Spec(A)
• 10 The Category of Schemes
• 11 Properties of Morphisms of Schemes
• 12 Modules, Algebras and Bundles on a Scheme
• 13 More Properties of Morphisms, Scheme Theoretic Image and the “Sorite”
• 14 Projective Schemes and Bundles
• 15 Further Properties of Morphisms
• 16 Conormal Sheaf and Projective Bundles
• 17 Cohomology Theory on Schemes
• 18 Intersection Theory
• 19 Characteristic Classes in Algebraic Geometry
• 20 The Riemann-Roch Theorem
• 21 Some Basic constructions in the category of projective kvarieties
• 22 More on Duality
• References
• Index.