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We characterize Hermitian cones among the surfaces of degree $q+1$ of $\text{PG}(3,q^{2})$ by their intersection numbers with planes. We then use this result and provide a characterization of nonsingular Hermitian varieties of $\text{PG}(4,q^{2})$ among quasi-Hermitian ones.

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The author was supported by the Italian National Group for Algebraic and Geometric Structures and their Applications (GNSAGA–INdAM).

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Journal of the Australian Mathematical Society
  • ISSN: 1446-7887
  • EISSN: 1446-8107
  • URL: /core/journals/journal-of-the-australian-mathematical-society
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