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Sulle ipersuperficie irriducibili d’ordine minimo che contengono tutti i punti di uno spazio di Galois \(S_{r,q}\). (Italian) Zbl 0106.35604
Denote by \(S_{r,q}\) the projective space of dimension \(r\) over a Galois field of order \(p^h=q\). The author considers the question of finding the irreducible hypersurfaces of \(S_{r,q}\) which exhaust the space. In the first section he gives the most general equation of such a hypersurface of order \(n\) and shows that such a hypersurface must have degree \(\geq q+1\). In the second section he considers the classification of curves of degree \(q+2\) in \(S_{2,q}\). The remaining sections give the projective classification of hypersurfaces of degree \(q+1\) and some geometric properties of hypersurfaces in \(S_{r,q}\).
Reviewer: K. R. Mount

14J70 Hypersurfaces and algebraic geometry
14G15 Finite ground fields in algebraic geometry
51E99 Finite geometry and special incidence structures