On a class of quasi-Hermitian surfaces in even characteristic
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arXiv
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| Format: | Preprint |
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2025
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| _version_ | 1866918115758047232 |
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| author | Aguglia, Angela Montinaro, Alessandro |
| author_facet | Aguglia, Angela Montinaro, Alessandro |
| contents | In [1], a new quasi-Hermitian variety $\mathcal{H}_\varepsilon^r$ in $\mathrm{PG}(r, q^2)$, with $q = 2^e$ and $e \geq 3$ an odd integer, was constructed. The variety depends on a primitive element $\varepsilon$ of the underlying field $\mathrm{GF}(q^2)$.11
In the present paper, we first provide a classification of such varieties up to projective equivalence in finite projective spaces of arbitrary dimension. Then, we focus on the case $r = 3$ and study the structure of the lines contained in $\mathcal{H}_\varepsilon^3$; as a consequence, we determine the full automorphism group of $\mathcal{H}_\varepsilon^3$ . Finally, as a byproduct, we prove the equivalence of certain minimal codes introduced in [3]. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2508_03907 |
| institution | arXiv |
| publishDate | 2025 |
| record_format | arxiv |
| spellingShingle | On a class of quasi-Hermitian surfaces in even characteristic Aguglia, Angela Montinaro, Alessandro Combinatorics Algebraic Geometry In [1], a new quasi-Hermitian variety $\mathcal{H}_\varepsilon^r$ in $\mathrm{PG}(r, q^2)$, with $q = 2^e$ and $e \geq 3$ an odd integer, was constructed. The variety depends on a primitive element $\varepsilon$ of the underlying field $\mathrm{GF}(q^2)$.11 In the present paper, we first provide a classification of such varieties up to projective equivalence in finite projective spaces of arbitrary dimension. Then, we focus on the case $r = 3$ and study the structure of the lines contained in $\mathcal{H}_\varepsilon^3$; as a consequence, we determine the full automorphism group of $\mathcal{H}_\varepsilon^3$ . Finally, as a byproduct, we prove the equivalence of certain minimal codes introduced in [3]. |
| title | On a class of quasi-Hermitian surfaces in even characteristic |
| topic | Combinatorics Algebraic Geometry |
| url | https://arxiv.org/abs/2508.03907 |