  If the complement of a closed convex set in a closed convex cone is bounded,
then this complement minus the apex of the cone is called a coconvex set.
Coconvex sets appear in singularity theory (they are closely related to Newton
diagrams) and in commutative algebra. Such invariants of coconvex sets as
volumes, mixed volumes, number of integer points, etc., play an important role.
This paper aims at extending various results from the theory of convex bodies
to the coconvex setting. These include the Aleksandrov-Fenchel inequality and
the Ehrhart duality.

Metric Geometry;Commutative Algebra;Combinatorics