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arXiv · 2212.05323

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

Anthony Saint-Criq
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Abstract

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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Anthony Saint-Criq. 2022-12-10. A Viro-Zvonilov-type inequality for Q-flexible curves of odd degree. https://doi.org/10.2140/pjm.2024.328.157

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