0
Prerequisites
▶
0.1
Affine Monoids
0.2
Tensor Product
0.3
Hopf algebras
▶
0.3.1
Group-like elements
0.3.2
Diagonalizable bialgebras
0.3.3
The group algebra functor
0.4
Category Theory
▶
0.4.1
Over category
0.4.2
Group objects
0.5
Group Schemes
▶
0.5.1
Correspondence between Hopf algebras and affine group schemes
0.5.2
Essential image of Spec on Hopf algebras
0.5.3
Diagonalisable groups
0.5.4
The Torus
1
Affine Toric Varieties
▶
1.1
Introduction to Affine Toric Varieties
▶
1.1.1
The Torus
1.1.2
The Definition of Affine Toric Variety
1.1.3
Lattice Points
1.1.4
Toric Ideals
1.1.5
Equivalence of Constructions
1.2
Cones and Affine Toric Varieties
▶
1.2.1
Convex Polyhedral Cones
1.2.2
Dual Cones and Faces
1.2.3
Relative Interiors
1.2.4
Strong Convexity
1.2.5
Separation
1.2.6
Rational Polyhedral Cones
1.2.7
Semigroup Algebras and Affine Toric Varieties
2
Bibliography
Dependency graph
Toric
Yaël Dillies, Paul Lezeau, Patrick Luo, Michał Mrugała, Justus Springer, Andrew Yang
0
Prerequisites
0.1
Affine Monoids
0.2
Tensor Product
0.3
Hopf algebras
0.3.1
Group-like elements
0.3.2
Diagonalizable bialgebras
0.3.3
The group algebra functor
0.4
Category Theory
0.4.1
Over category
0.4.2
Group objects
0.5
Group Schemes
0.5.1
Correspondence between Hopf algebras and affine group schemes
0.5.2
Essential image of Spec on Hopf algebras
0.5.3
Diagonalisable groups
0.5.4
The Torus
1
Affine Toric Varieties
1.1
Introduction to Affine Toric Varieties
1.1.1
The Torus
1.1.2
The Definition of Affine Toric Variety
1.1.3
Lattice Points
1.1.4
Toric Ideals
1.1.5
Equivalence of Constructions
1.2
Cones and Affine Toric Varieties
1.2.1
Convex Polyhedral Cones
1.2.2
Dual Cones and Faces
1.2.3
Relative Interiors
1.2.4
Strong Convexity
1.2.5
Separation
1.2.6
Rational Polyhedral Cones
1.2.7
Semigroup Algebras and Affine Toric Varieties
2
Bibliography