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arXiv · 2605.27623

Contact Invariants for Plane Curves in a Pencil

Ciro Ciliberto·Rick Miranda·Joaquim Roe
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Abstract

Let $\calP$ be a general pencil of curves of degree $d$ in the projective plane. In this paper we review the computation of the number of curves in $\calP$ that have a hyperflex line, a flex bitangent line or a tritangent line. Then we focus on the curves in the dual plane described by the flex tangents and the bitangents of the curves of $\calP$ and the curves in the original plane described by the flexes and the points of bitangencies of the curves in $\calP$. Some of these curves have been studied already: we mainly focus here on the ones that still have not been treated systematically, and we compute their degree, genus, and singularities.

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Ciro Ciliberto, Rick Miranda, Joaquim Roe. 2026-05-26. Contact Invariants for Plane Curves in a Pencil. https://arxiv.org/abs/2605.27623

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