Pencils of plane cubics with one base point

Abstract

We study pencils of plane cubics with only one base point and general member smooth, giving a complete classification. Under the additional hypothesis that all members are irreducible, we prove that there exists a unique non-isotrivial pencil with these properties up to projective transformation. We compare our construction with the classical approaches given by Gattazzo, Beauville and Miranda-Persson.

18 pages, 9 figures. This is an expanded revised version with respect to the one accepted in Rendiconti del Circolo Matematico di Palermo Series 2