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arXiv · 2409.14727

On the double tangent of projective closed curves

Thomas Blomme
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Abstract

We generalize a previous result by Fabricius-Bjerre from curves in $\mathbb R^2$ to curves in $\mathbb R P^2$. Applied to the case of real algebraic curves, this recovers the signed count of bitangents of quartics introduced by Larson-Vogt and proves its positivity, conjectured by Larson-Vogt. Our method is not specific to quartics and applies to algebraic curves of any degree.

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Thomas Blomme. 2024-09-23. On the double tangent of projective closed curves. https://arxiv.org/abs/2409.14727

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