Algebraic Geometry

The algebraic geometry module includes machinery for studying general algebraic varieties and families of special curves (e.g. elliptic curves). The major categories include:

• Schemes and maps of schemes
• Rational scrolls
• Zero-dimensional schemes
• Algebraic curves
• Function fields and differentials of plane curves
• Divisor groups of plane curves
• Resolution graphs and splice diagrams
• Newton polygons
• Plane conic curves and general rational curves
• Elliptic curves
• Hyperelliptic curves
• Modular symbols
• Brandt modules
• Modular forms
• Modular curves
• Database of K3 surfaces