Characteristic linear system of an algebraic family of curves

In modern terms, it is a subsystem of the linear system associated to the normal bundle to [math]\displaystyle{ C \hookrightarrow Y }[/math]. 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.

References

• Enrico Arbarello, Maurizio Cornalba, and Phillip Griffiths, Geometry of algebraic curves. Vol. II, with a contribution by Joseph Daniel Harris, Grundlehren der Mathematischen Wissenschaften, vol. 268, Springer, Heidelberg, 2011. MR2807457 doi:10.1007/978-1-4757-5323-3