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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

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