Discrete automorphism groups of convex cones of finite type

Abstract

We investigate subgroups of SL (n,Z) which preserve an open nondegenerate convex cone in real n-space and admit in that cone as fundamental domain a polyhedral cone of which some faces are allowed to lie on the boundary. Examples are arithmetic groups acting on selfdual cones, Weyl groups of certain Kac-Moody algebras and do occur in algebraic geometry as the automorphism groups of projective manifolds acting on their ample cones.

30 pages, to appear in Compositio Math

References in corpus (2)

• Compactifications of moduli spaces inspired by mirror symmetry
• The cone conjecture for Calabi-Yau pairs in dimension two

Cited by in corpus (7)

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• A proof of the Kawamata-Morrison Cone Conjecture for holomorphic symplectic varieties of K3^[n] or generalized Kummer deformation type
• Faces of highest weight modules and the universal Weyl polyhedron
• Zero entropy automorphisms of compact Kähler manifolds and dynamical filtrations
• The stable cohomology of the Satake compactification of ${\mathcal{A}}_g$
• A cone conjecture for log Calabi-Yau surfaces