Geodesic
Forms of del~Pezzo surfaces of degree~$5$ and~$6$
Sbornik. Mathematics, Tome 214 (2023) no. 6, pp. 816-831

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We obtain necessary and sufficient condition for the existence of del Pezzo surfaces of degrees $5$ and $6$ over a field $K$ with a prescribed action of absolute Galois group $\operatorname{Gal}(K^{\mathrm{sep}}/K)$ on the graph of $(-1)$-curves. We also compute the automorphism groups of del Pezzo surfaces of degree $5$ over arbitrary fields. Bibliography: 19 titles.
Keywords: automorphism groups.
Mots-clés : del Pezzo surface 
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     title = {Forms of {del~Pezzo} surfaces of degree~$5$ and~$6$},
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A. V. Zaitsev. Forms of del~Pezzo surfaces of degree~$5$ and~$6$. Sbornik. Mathematics, Tome 214 (2023) no. 6, pp. 816-831. http://geodesic.mathdoc.fr/item/SM_2023_214_6_a2/