Pencils of plane cubics with one base point

• DOI: 10.48550/arxiv.2407.04569
• Publication Date: 2025-01-03
• Authors: Riccardo Moschetti; Gian Pietro Pirola; Lidia Stoppino
• Keywords: Mathematics - Algebraic Geometry; 14C21, 14H50, 14H10; FOS: Mathematics; Algebraic Geometry (math.AG)

18 pages, 9 figures. Revised version. New references and Remark 6.2 added. Comments welcome!<br/>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.<br/>