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===Linear system of conics===
{{main|Linear system of conics}}
===Characteristic linear system of a family of curves===
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 of divisors|linear system]] formed by the curves in the family that are infinitely near ''C''.<ref>{{cite book |last1=Arbarello |first1=Enrico |author1-link=Enrico Arbarello |last2=Cornalba |first2=Maurizio |last3=Griffiths |first3=Phillip |author3-link=Phillip Griffiths |title=Geometry of algebraic curves |volume=II, with a contribution by Joseph Daniel Harris |series=Grundlehren der Mathematischen Wissenschaften |issue=268 |publisher=Springer |___location=Heidelberg |year=2011 |mr=2807457 |doi=10.1007/978-1-4757-5323-3 |page=3}}</ref>
In modern terms, it is a subsystem of the linear system associated to the [[normal bundle]] to <math>C \hookrightarrow Y</math>. Note a characteristic system need not 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.
=== Other examples ===
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