A note on the stability of pencils of plane curves
The semisimple group \(PGL(3)\) acts on the set of all degree \(d\) complex plane curves and on the set of all pencils of degree \(d\) plane curves. The author uses the log canonical threshold to give explicit criteria for the stability or semistability of a pencil \(P\) in terms of the stability or semistability of its members. The pencil \(P\) is semistable (resp. stable) if all its members \(C_d\in P\) are semistable (resp. stable). The pencil \(P\) is stable if all its members are semistable and at most one \(C_d\in P\) is strictly semistable. The author gives a criterion for the stability of \(P\) when \(2\) of its members are strictly semistable.
scientific article; zbMATH DE number 7461064