On the Fine Interior of Three-dimensional Canonical Fano Polytopes

Abstract

The Fine interior $\Delta^{\text{FI}}$ of a $d$-dimensional lattice polytope $\Delta$ is a rational subpolytope of $\Delta$ which is important for constructing minimal birational models of non-degenerate hypersurfaces defined by Laurent polynomials with Newton polytope $\Delta$. This paper presents some computational results on the Fine interior of all $674,\!688$ three-dimensional canonical Fano polytopes.