  Generalizing the famous Bernstein-Kushnirenko Theorem, Khovanskii proved in
1978 a combinatorial formula for the arithmetic genus of the compactification
of a generic complete intersection associated to a family of lattice polytopes.
Recently, an analogous combinatorial formula, called the discrete mixed volume,
was introduced by Bihan and shown to be nonnegative. By making a footnote of
Khovanskii in his paper explicit, we interpret this invariant as the (motivic)
arithmetic genus of the non-compact generic complete intersection associated to
the family of lattice polytopes.
