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The characterization of Hermitian surfaces by the number of points. (English) Zbl 1410.11081
Summary: The nonsingular Hermitian surface of degree \({\sqrt{q} +1}\) is characterized by its number of \({\mathbb{F}_q}\) -points among the surfaces over \({\mathbb{F}_q}\) of degree \({\sqrt{q} +1}\) in the projective 3-space without \({\mathbb{F}_q}\) -plane components.

MSC:
11G25 Varieties over finite and local fields
14G15 Finite ground fields in algebraic geometry
14J70 Hypersurfaces and algebraic geometry
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