On certain extremal pencils of curves with respect to the total reducibility order

Abstract

We consider another application of the Ogg-Shafarevich-Grothendieck formula (abbr. OSG) to pencils of plane curves of degree $d$ with certain extremal properties of reducibility. Besides some new results for extremal pencils we treat also various aspects of the topics, e.g. pencils with small number of special fibres, families with $(2IV_{d})$, etc.