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 $${\mathbb {Z}}$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mi>Z</mml:mi> </mml:math> . Moreover, we give an explicit description of the boundary of the movable cone $${{\,\mathrm{{\overline{Mov}}}\,}}(X)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mspace/> <mml:mover> <mml:mi>Mov</mml:mi> <mml:mo>¯</mml:mo> </mml:mover> <mml:mspace/> </mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> </mml:math> . 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 $${{\,\textrm{Bir}\,}}(X)$$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mrow> <mml:mspace/> <mml:mtext>Bir</mml:mtext> <mml:mspace/> </mml:mrow> <mml:mo>(</mml:mo> <mml:mi>X</mml:mi> <mml:mo>)</mml:mo> </mml:mrow> </mml:math> .