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Forms of del Pezzo Surfaces

Student: Zaitsev Aleksandr

Supervisor: Konstantin Shramov

Faculty: Faculty of Mathematics

Educational Programme: Mathematics (Bachelor)

Year of Graduation: 2021

In this paper, we obtain a necessary and sufficient condition for the existence of del Pezzo surfaces of degrees 5 and 6 over a field $K$ with a given action of the absolute Galois group $\text{Gal} ( K^{\sep}/K )$ on the graph of $(-1)$"~curves. Automorphism groups of del Pezzo surfaces of degree 5 over arbitrary fields are also calculated.

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