2008/09/10 by Treutlein, Jaron · 1 citation
#14M25 #52B20 #Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics
paper · doi:10.48550/arxiv.0809.1787
A theorem of Howe states that every 3-dimensional lattice polytope P whose only lattice points are its vertices, is a Cayley polytope, i.e. P is the convex hull of two lattice polygons with distance one. We want to generalize this result by classifying 3-dimensional lattice polytopes without interior lattice points. The main result will be, that they are up to finite many exceptions either Cayley polytopes or there is a projection, which maps the polytope to the double unimodular 2-simplex. To every such polytope we associate a smooth projective surface of genus 0.