On the combinatorial classification of toric log del Pezzo surfaces

Abstract

AbstractToric log del Pezzo surfaces correspond to convex lattice polygons containing the origin in their interior and having only primitive vertices. Upper bounds on the volume and on the number of boundary lattice points of these polygons are derived in terms of the indexℓ. Techniques for classifying these polygons are also described: a direct classification for index two is given, and a classification for allℓ≤16 is obtained.