Decomposition problem on endomorphisms of projective varieties
Let \(X, Y\) be non singular projective varieties \((\dim(Y) = 2,3)\), with \(K_X\) nef and \(K_Y\) not nef, let \(Z = X\times Y\) and \(q : Z \to Y\) be the projection. Suppose that there exists an endomorphism \(f: Z\to Z\) which is not an isomorphism. The author proves that, under suitable conditions concerning the extremal rays of \(Y\), for some integer \(k > 0\), \(f^k\) induces an automorphism \(g : Y\to Y\) such that \(q\circ f^k =g\circ q\).
scientific article; zbMATH DE number 2114253