Birational automorphism groups and the movable cone theorem for Calabi–Yau complete intersections of products of projective spaces

Abstract

For a Calabi-Yau manifold X, the Kawamata – Morrison movable cone conjecture connects the convex geometry of the movable cone Mov‾(X) to the birational automorphism group. Using the theory of Coxeter groups, Cantat and Oguiso proved that the conjecture is true for general varieties of Wehler type, and they described explicitly Bir(X). We generalize their argument to prove the conjecture and describe Bir(X) for general complete intersections of ample divisors in arbitrary products of projective spaces. Then, under a certain condition, we give a description of the boundary of Mov‾(X) and an application connected to the numerical dimension of divisors.