Fixed part of a linear system ($F$)

For a nonempty complete linear system of a divisor on a smooth projective variety, the coefficient of a prime divisor in its fixed part is the minimum of its multiplicities in all members. Multiplication by the section of $F$ identifies the sections of $D-F$ with those of $D$.

A fixed component is a prime divisor appearing in every member of a complete linear system of a divisor. This concerns divisorial components; a linear system can have isolated basepoints even when it has no fixed component.