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 $\overline{\mathrm{Mov}}(X)$ 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 $\mathrm{Bir}(X)$. We generalize their argument to prove the conjecture and describe $\mathrm{Bir}(X)$ 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 $\overline{\mathrm{Mov}}(X)$ and an application connected to the numerical dimension of divisors.

22 pages, 2 figures

References in corpus (1)

• The movable cone of certain Calabi-Yau threefolds of Picard number two

Cited by in corpus (3)

• On numerical dimensions of Calabi--Yau varieties
• The movable cone of Calabi--Yau threefolds in ruled Fano manifolds
• The volume of a divisor and cusp excursions of geodesics in hyperbolic manifolds