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Article Dans Une Revue Pacific Journal of Mathematics Année : 2024

A Viro–Zvonilov-type inequality for Q-flexible curves of odd degree

Résumé

We define an analogue of the Arnold surface for odd degree flexible curves, and we use it to double branch cover Q-flexible embeddings, where Q-flexible is a condition to be added to the classical notion of a flexible curve. This allows us to obtain a Viro--Zvonilov-type inequality: an upper bound on the number of non-empty ovals of a curve of odd degree. We investigate our method for flexible curves in a quadric to derive a similar bound in two cases. We also digress around a possible definition of non-orientable flexible curves, for which our method still works and a similar inequality holds.
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hal-04550270 , version 1 (17-04-2024)

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Anthony Saint-Criq. A Viro–Zvonilov-type inequality for Q-flexible curves of odd degree. Pacific Journal of Mathematics, 2024, 328 (1), pp.157-192. ⟨10.2140/pjm.2024.328.157⟩. ⟨hal-04550270⟩
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