The aim was to give many interesting examples of Q-homology projective planes. They occur when w * = 1. For that case, we prove that Kollár surfaces are Hwang-Keum [HK12] surfaces. For w * > 1, we construct a geometrically explicit birational map between Kollár surfaces and cyclic covers z w * = l a 2 a 3 a 4

We study Calabi-Yau manifolds which are complete intersections of hypersurfaces of multidegree 1 in an m-fold product of n-dimensional projective spaces. Using the theory of Coxeter groups, we show that the birational automorphism group of such a Calabi-Yau manifold X is infinite and a free product of copies of Z . Moreover, we give an explicit description of the boundary of the movable cone Mov(X). In the end, we consider examples for the general and non-general case and picture the movable cone and the fundamental domain for the action of Bir(X).

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