Algebraic Geometry#

Schemes

Ambient spaces, scheme creation and basic scheme operations.

Coherent Sheaves

Sheaf creation, accessors and sheaf homomorphisms.

Algebraic Curves

Curve ambients, local and global properties, and maps between curves.

Resolution Graphs and Splice Diagrams

Resolution graphs, splice diagrams and translation between them.

Algebraic Surfaces

Surface schemes, resolution by blow-up and surfaces in projective space.

Riemann Surfaces

Riemann surface creation, points, divisors and the Abel-Jacobi map.

Hilbert Series of Polarised Varieties

Hilbert series, baskets of singularities and polarised varieties.

Toric Varieties

Toric fans, cones, Cox rings and toric divisors.