# Algebraic Geometry

SchemesAmbient spaces, scheme creation and basic scheme operations.

[Schemes](Schemes/index-schemes.md)Coherent SheavesSheaf creation, accessors and sheaf homomorphisms.

[Coherent Sheaves](Sheaves/index-sheaves.md)Algebraic CurvesCurve ambients, local and global properties, and maps between curves.

[Algebraic Curves](AlgebraicCurves/index-algebraic-curves.md)Resolution Graphs and Splice DiagramsResolution graphs, splice diagrams and translation between them.

[Resolution Graphs and Splice Diagrams](ResolutionGraphsAndSpliceDiagrams/index-resolution-graphs-and-splice-diagrams.md)Algebraic SurfacesSurface schemes, resolution by blow-up and surfaces in projective space.

[Algebraic Surfaces](AlgebraicSurfaces/index-algebraic-surfaces.md)Riemann SurfacesRiemann surface creation, points, divisors and the Abel-Jacobi map.

[Riemann Surfaces](RiemannSurfaces/index-riemann-surfaces.md)Hilbert Series of Polarised VarietiesHilbert series, baskets of singularities and polarised varieties.

[Hilbert Series of Polarised Varieties](HilbertSeriesOfPolarisedVarieties/index-hilbert-series-of-polarised-varieties.md)Toric VarietiesToric fans, cones, Cox rings and toric divisors.

[Toric Varieties](ToricVarieties/index-toric-varieties.md)