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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
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