Schemes

• Scheme implementation overview
  • TODO List
• Schemes
• The Spec functor
• Scheme obtained by gluing two other schemes
• Points on schemes
• Ambient Spaces
• Algebraic schemes
• Hypersurfaces in affine and projective space
• Set of homomorphisms between two schemes
• Scheme morphism
• Divisors on schemes
• Divisor groups

Affine Schemes

• Affine \(n\) space over a ring
• Points on affine varieties
• Morphisms on affine varieties
• Enumeration of rational points on affine schemes
• Set of homomorphisms between two affine schemes

Projective Schemes

• Projective \(n\) space over a ring
• Points on projective varieties
• Morphisms on projective varieties
• Enumeration of rational points on projective schemes
• Set of homomorphisms between two projective schemes
• Automorphism groups of endomorphisms of the projective line
• Sage functions to compute minimal models of rational functions

Products of Projective Spaces

• Products of projective spaces
• Set of homomorphisms
• Polynomial morphisms for products of projective spaces
• Points for products of projective spaces
• Wehler K3 Surfaces

Toric Varieties

• Toric varieties
• Fano toric varieties
• Library of toric varieties
• Toric divisors and divisor classes
• Toric rational divisor classes
• The Chow group of a toric variety
• Toric ideals
• Morphisms of Toric Varieties
  • Fibrations
• Weierstrass form of a toric elliptic curve.
• Map to the Weierstrass form of a toric elliptic curve.
• Weierstrass for Elliptic Curves in Higher Codimension
• Set of homomorphisms between two toric varieties.
• Enumerate Points of a Toric Variety
• Construct sheaves on toric varieties.
• Klyachko Bundles and Sheaves.

Indices and Tables

• Index
• Module Index
• Search Page