ИСТИНА

Let Crn (k) be the Cremona group in n variables and let G ⊂ Crn (k) be a group of order two. We may assume that G acts biregularly on a smooth projective variety X so that the embedding G ⊂ Crn (k) is induced by the action of G on the function field k(X). Suppose that there exists a non-uniruled component S of the G-fixed point locus. It is easy to see that there exists at most one such a component and the birational type of S does not depend on the choice of our smooth model X. This allow to introduce the notion of Kodaira dimension of G. Using the equivariant minimal model program we give a very rough classification of subgroups G ⊂ Cr3 (k) of non-negative Kodaira dimension.