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| Main Authors: | , , , |
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| Format: | Preprint |
| Published: |
2023
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2307.03542 |
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| _version_ | 1866917601293107200 |
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| author | Adriaensen, Sam De Beule, Jan Grimaldi, Giovanni Giuseppe Mannaert, Jonathan |
| author_facet | Adriaensen, Sam De Beule, Jan Grimaldi, Giovanni Giuseppe Mannaert, Jonathan |
| contents | In this paper, we provide a construction of $(q+1)$-ovoids of the hyperbolic quadric $Q^+(7,q)$, $q$ an odd prime power, by glueing $(q+1)/2$-ovoids of the elliptic quadric $Q^-(5,q)$. This is possible by controlling some intersection properties of (putative) $m$-ovoids of elliptic quadrics. It yields eventually $(q+1)$-ovoids of $Q^+(7,q)$ not coming from a $1$-system. Secondly, we also construct $m$-ovoids for $m \in \{ 2,4,6,8,10\}$ in $Q^+(7,3)$. Therefore we first investigate how to construct spreads of $\pg(3,q)$ that have as many secants to an elliptic quadric as possible. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2307_03542 |
| institution | arXiv |
| publishDate | 2023 |
| record_format | arxiv |
| spellingShingle | On $m$-ovoids of $Q^+(7,q)$ with $q$ odd Adriaensen, Sam De Beule, Jan Grimaldi, Giovanni Giuseppe Mannaert, Jonathan Combinatorics In this paper, we provide a construction of $(q+1)$-ovoids of the hyperbolic quadric $Q^+(7,q)$, $q$ an odd prime power, by glueing $(q+1)/2$-ovoids of the elliptic quadric $Q^-(5,q)$. This is possible by controlling some intersection properties of (putative) $m$-ovoids of elliptic quadrics. It yields eventually $(q+1)$-ovoids of $Q^+(7,q)$ not coming from a $1$-system. Secondly, we also construct $m$-ovoids for $m \in \{ 2,4,6,8,10\}$ in $Q^+(7,3)$. Therefore we first investigate how to construct spreads of $\pg(3,q)$ that have as many secants to an elliptic quadric as possible. |
| title | On $m$-ovoids of $Q^+(7,q)$ with $q$ odd |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2307.03542 |