Birational automorphism groups of projective varieties of Picard number two

We slightly extend a result of Oguiso on birational or automorphism groups (resp. of Lazi\'c - Peternell on Morrison-Kawamata cone conjecture) from Calabi-Yau manifolds of Picard number two to arbitrary singular varieties X (resp. to klt Calabi-Yau pairs in broad sense) of Picard number two. When X has only klt singularities and is not a complex torus, we show that either Aut(X) is almost cyclic, or it has only finitely many connected components.Comment: title slightly changed to this; some proof simplified; submitted to the Proceedings of Groups of Automorphisms in Birational and Affine Geometry, 28 October - 3 November 2012, C.I.R.M., Trento, Ital