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## Quotients of del Pezzo Surfaces of Degree 2

Moscow Mathematical Journal. 2018. Vol. 18. No. 3. P. 557-597.

Let 𝕜 be any field of characteristic zero, X be a del Pezzo surface of degree 2 and G be a group acting on X. In this paper we study 𝕜-rationality questions for the quotient surface X/G. If there are no smooth 𝕜-points on X/G then X/G is obviously non-𝕜-rational. Assume that the set of smooth 𝕜-points on the quotient is not empty. We find a list of groups such that the quotient surface can be non-𝕜-rational. For these groups we construct examples of both 𝕜-rational and non-𝕜-rational quotients of both 𝕜-rational and non-𝕜-rational del Pezzo surfaces of degree 2 such that the G-invariant Picard number of X is 1. For all other groups we show that the quotient X/G is always 𝕜-rational.