On certain extremal pencils of curves with respect to the total reducibility order. (English) Zbl 1328.14012

Nguyen Khac Viet

Proc. Japan Acad., Ser. A 87, No. 10, 194-198 (2011).

Summary: 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.

MSC:

14C21	Pencils, nets, webs in algebraic geometry
14H10	Families, moduli of curves (algebraic)

Keywords:

extremal pencils; total reducibility order; Ogg-Shafarevich-Grothendieck formula

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