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Toric log del Pezzo surfaces correspond to convex lattice polygons containingthe origin in their interior and having only primitive vertices. An upper boundon the volume and on the number of boundary lattice points of these polygons isderived in terms of the index l. Techniques for classifying these polygons arealso described: a direct classification for index two is given, and aclassification for all l<17 is obtained.

On the combinatorial classification of toric log del Pezzo surfaces