  In this paper we show that the spectrum of the Q-codegree of a d-dimensional
lattice polytope is finite above any positive threshold in the class of lattice
polytopes with \alpha-canonical normal fan for any fixed \alpha>0. For
\alpha=1/r this includes lattice polytopes with Q-Gorenstein normal fan of
index r. In particular, this proves Fujita's Spectrum Conjecture for polarized
varieties in the case of Q-Gorenstein toric varieties of index r.

Combinatorics;Algebraic Geometry