On the combinatorial classification of toric log del Pezzo surfaces

Abstract

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

16 pages

Cited by in corpus (10)

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• Chern-Simons: Fano and Calabi-Yau
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• Reflexive polytopes of higher index and the number 12
• Minimality and mutation-equivalence of polygons
• Stringy $E$-functions of canonical toric Fano threefolds and their applications
• Classifying log del Pezzo surfaces with torus action
• Del Pezzo surfaces of Picard number one admitting a torus action