A Royal Road to Algebraic Geometry

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...

Descripción completa

Detalles Bibliográficos
Clasificación:Libro Electrónico
Autor principal: Holme, Audun (Autor)
Autor Corporativo: SpringerLink (Online service)
Formato: Electrónico eBook
Idioma:Inglés
Publicado: Berlin, Heidelberg : Springer Berlin Heidelberg : Imprint: Springer, 2012.
Edición:1st ed. 2012.
Temas:
Algebraic geometry.
Algebra, Homological.
Geometry.
Algebraic topology.
Commutative algebra.
Commutative rings.
Mathematics.
History.
Algebraic Geometry.
Category Theory, Homological Algebra.
Algebraic Topology.
Commutative Rings and Algebras.
History of Mathematical Sciences.
Acceso en línea:Texto Completo
Tabla de Contenidos:
  • 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.

Ejemplares similares