Finiteness of the polyhedral Q-codegree spectrum

Abstract

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 α-canonical normal fan for any fixed α>0. For α=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.

9 pages