Pencils of plane cubics with one base point
Algebraic Geometry
2025-08-04 v3
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.
Cite
@article{arxiv.2407.04569,
title = {Pencils of plane cubics with one base point},
author = {Riccardo Moschetti and Gian Pietro Pirola and Lidia Stoppino},
journal= {arXiv preprint arXiv:2407.04569},
year = {2025}
}
Comments
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