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 irre- ducible, we prove that there exists a unique non-isotrivial pencil with these properties up to projective transformations. We compare our construction with the classical approaches given by Gattazzo, Beauville and Miranda-Persson.
Pencils of plane cubics with one base point
Riccardo Moschetti
;Gian Pietro Pirola;Lidia Stoppino
2025-01-01
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 irre- ducible, we prove that there exists a unique non-isotrivial pencil with these properties up to projective transformations. We compare our construction with the classical approaches given by Gattazzo, Beauville and Miranda-Persson.File in questo prodotto:
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