Movable cones of complete intersections of multidegree one on products of projective spaces

Abstract

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 $\mathbb{Z}$ . Moreover, we give an explicit description of the boundary of the movable cone $\overline{\operatorname{Mov}}(X)$. 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 $\operatorname{Bir}(X)$.