# Schemes¶

## 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¶

## 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
- 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.