Schemes: Linear Systems

The complete linear system on ${\bf P}$ of degree d is the collection of all homogeneous polynomials of degree d on ${\bf P}$, or equivalently, the degree d hypersurfaces thereby defined. A general linear system corresponds to some vector subspace of the coefficient space of a complete linear system.

• Creation of a linear system explicitly
• Creation of a linear system satisfying geometric conditions
• Properties: Sections, degree, dimension, base scheme
• Properties: Base component, base points, generic multiplicity at a point
• Complement with respect to a subsystem or scheme
• Intersection
• Maps of a linear system