Forms of del Pezzo surfaces of degree 5 and 6

Alexandr Zaitsev

Forms of del Pezzo surfaces of degree 5 and 6

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arxiv 2302.04937 v1 pith:RQ6WZ3MR submitted 2023-02-09 math.AG

Alexandr Zaitsev This is my paper · ORCID

classification math.AG

keywords degreepezzosurfacestextabsoluteactionarbitraryautomorphism

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abstract

In this paper we obtain necessary and sufficient condition for existence of del Pezzo surfaces of degree $5$ and $6$ over a field $K$ with a prescribed action of absolute Galois group $\text{Gal} ( K^{\text{sep}}/K)$ on the graph of $(-1)$-curves. Also we compute automorphism groups of del Pezzo surfaces of degree $5$ over arbitrary fields.

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