Characteristic linear system of an algebraic family of curves
In algebraic geometry, the characteristic linear system of a family of curves on an algebraic surface Y for a curve C in the family is a linear system formed by the curves in the family that are infinitely near C.
In modern terms, it is a subsystem of the linear system associated to the normal bundle to. Note a characteristic system need to be complete; in fact, the question of completeness is something studied extensively by the Italian school without a satisfactory conclusion; nowadays, the Kodaira–Spencer theory can be used to answer the question of the completeness.
