• 1 Category theory ▶
    • 1.1 Over category
    • 1.2 Objects ▶
      • 1.2.1 Group objects
      • 1.2.2 Module objects
  • 2 Algebra ▶
    • 2.1 Tensor Product
    • 2.2 Affine Monoids
    • 2.3 Hopf algebras ▶
      • 2.3.1 Ideals and quotients
      • 2.3.2 Group algebras
      • 2.3.3 Group-like elements
      • 2.3.4 Diagonalizable bialgebras
      • 2.3.5 The group algebra functor
  • 3 Convex geometry ▶
    • 3.1 Cones ▶
      • 3.1.1 Convex Polyhedral Cones
      • 3.1.2 Dual Cones and Faces
      • 3.1.3 Relative Interiors
      • 3.1.4 Strong Convexity
      • 3.1.5 Separation
      • 3.1.6 Rational Polyhedral Cones
      • 3.1.7 Semigroup Algebras and Affine Toric Varieties
  • 4 Scheme theory ▶
    • 4.1 Correspondence between affine group schemes and Hopf algebras ▶
      • 4.1.1 Spec of an algebra
      • 4.1.2 Spec of a bialgebra
      • 4.1.3 Spec of a Hopf algebra
      • 4.1.4 Essential image of Spec on Hopf algebras
    • 4.2 Diagonalisable groups
    • 4.3 The torus
  • 5 Toric varieties ▶
    • 5.1 Toric varieties
    • 5.2 Affine toric varieties and affine monoids ▶
      • 5.2.1 Toric varieties from affine monoids
      • 5.2.2 Essential surjectivity from affine monoids to affine toric varieties
    • 5.3 Affine toric varieties and toric ideals ▶
      • 5.3.1 Toric ideals and affine monoids
  • 6 Bibliography
  • Dependency graph

Toric

Yaël Dillies, Paul Lezeau, Patrick Luo, Michał Mrugała, Justus Springer, Andrew Yang

The presentation is inspired by [ 1 ] , but we do not aim to follow it very closely. For example, the chapters below do not match those of [ 1 ] .

  • 1 Category theory
    • 1.1 Over category
    • 1.2 Objects
      • 1.2.1 Group objects
      • 1.2.2 Module objects
  • 2 Algebra
    • 2.1 Tensor Product
    • 2.2 Affine Monoids
    • 2.3 Hopf algebras
      • 2.3.1 Ideals and quotients
      • 2.3.2 Group algebras
      • 2.3.3 Group-like elements
      • 2.3.4 Diagonalizable bialgebras
      • 2.3.5 The group algebra functor
  • 3 Convex geometry
    • 3.1 Cones
      • 3.1.1 Convex Polyhedral Cones
      • 3.1.2 Dual Cones and Faces
      • 3.1.3 Relative Interiors
      • 3.1.4 Strong Convexity
      • 3.1.5 Separation
      • 3.1.6 Rational Polyhedral Cones
      • 3.1.7 Semigroup Algebras and Affine Toric Varieties
  • 4 Scheme theory
    • 4.1 Correspondence between affine group schemes and Hopf algebras
      • 4.1.1 Spec of an algebra
      • 4.1.2 Spec of a bialgebra
      • 4.1.3 Spec of a Hopf algebra
      • 4.1.4 Essential image of Spec on Hopf algebras
    • 4.2 Diagonalisable groups
    • 4.3 The torus
  • 5 Toric varieties
    • 5.1 Toric varieties
    • 5.2 Affine toric varieties and affine monoids
      • 5.2.1 Toric varieties from affine monoids
      • 5.2.2 Essential surjectivity from affine monoids to affine toric varieties
    • 5.3 Affine toric varieties and toric ideals
      • 5.3.1 Toric ideals and affine monoids
  • 6 Bibliography