在投影闭合曲线的重切线上

IF 0.9 3区数学 Q2 MATHEMATICS

Bulletin of the London Mathematical Society Pub Date : 2025-04-02 DOI:10.1112/blms.70061

Thomas Blomme

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引用次数: 0

摘要

我们推广了fabicius - bjerre[数学]先前的结果。Scand. 11 (1962), no。[2]从r2 $\mathbb {R}^2$中的曲线到r2 $\mathbb {R}P^2$中的曲线。应用于实代数曲线的情况下，恢复了Larson-Vogt [Res. Math]引入的四分位数的有符号计数。科学通报8 (2021),no。[26]并证明了Larson-Vogt猜想的正性。我们的方法不是特定于四分之一，适用于任何程度的代数曲线。

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On the double tangent of projective closed curves

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On the double tangent of projective closed curves

We generalize a previous result by Fabricius–Bjerre [Math. Scand. 11 (1962), no. 2, 113–116] from curves in $R^{2}$ to curves in $R P^{2}$ . Applied to the case of real algebraic curves, this recovers the signed count of bitangents of quartics introduced by Larson–Vogt [Res. Math. Sci. 8 (2021), no. 26] and proves its positivity, conjectured by Larson–Vogt. Our method is not specific to quartics and applies to algebraic curves of any degree.