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| Main Authors: | , |
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| Format: | Preprint |
| Published: |
2026
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| Subjects: | |
| Online Access: | https://arxiv.org/abs/2603.01738 |
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| _version_ | 1866914426293059584 |
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| author | Aguglia, Angela Siconolfi, Viola |
| author_facet | Aguglia, Angela Siconolfi, Viola |
| contents | Quasi-Hermitian varieties arise as higher-dimensional generalizations of non-classical unitals, including the Buekenhout--Metz (BM) and Buekenhout--Tits (BT) families.
After reviewing known constructions and structural properties, we determine explicitly the BC representation of BM and BT quasi-Hermitian varieties in $\mathrm{PG}(3,q^2)$ inside $\mathrm{PG}(6,q)$. We show that BM varieties correspond to quadratic cones with hyperbolic base, whereas BT varieties give rise to non-quadratic cones, and we describe the associated configuration of spread elements in the section at infinity.
These results provide a geometric interpretation of the non-classical nature of BM and BT varieties within the BC framework. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_01738 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Quasi-Hermitian Varieties and Their Barlotti--Cofman Representation Aguglia, Angela Siconolfi, Viola Combinatorics Quasi-Hermitian varieties arise as higher-dimensional generalizations of non-classical unitals, including the Buekenhout--Metz (BM) and Buekenhout--Tits (BT) families. After reviewing known constructions and structural properties, we determine explicitly the BC representation of BM and BT quasi-Hermitian varieties in $\mathrm{PG}(3,q^2)$ inside $\mathrm{PG}(6,q)$. We show that BM varieties correspond to quadratic cones with hyperbolic base, whereas BT varieties give rise to non-quadratic cones, and we describe the associated configuration of spread elements in the section at infinity. These results provide a geometric interpretation of the non-classical nature of BM and BT varieties within the BC framework. |
| title | Quasi-Hermitian Varieties and Their Barlotti--Cofman Representation |
| topic | Combinatorics |
| url | https://arxiv.org/abs/2603.01738 |