A Viro-Zvonilov-type inequality for Q-flexible curves of odd degree
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arXiv
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| Format: | Preprint |
| Published: |
2022
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| _version_ | 1866929314400829440 |
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| author | Saint-Criq, Anthony |
| author_facet | Saint-Criq, Anthony |
| contents | 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. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2212_05323 |
| institution | arXiv |
| publishDate | 2022 |
| record_format | arxiv |
| spellingShingle | A Viro-Zvonilov-type inequality for Q-flexible curves of odd degree Saint-Criq, Anthony Algebraic Geometry Geometric Topology 14P25, 57M12 (Primary) 14H45, 57S25 (Secondary) 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. |
| title | A Viro-Zvonilov-type inequality for Q-flexible curves of odd degree |
| topic | Algebraic Geometry Geometric Topology 14P25, 57M12 (Primary) 14H45, 57S25 (Secondary) |
| url | https://arxiv.org/abs/2212.05323 |