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On the combinatorial classification of toric log del Pezzo surfaces

Published online by Cambridge University Press:  01 January 2010

Alexander M. Kasprzyk
Affiliation:
School of Mathematics and Statistics, University of Sydney, Sydney, NSW 2006, Australia (email: a.m.kasprzyk@usyd.edu.au)
Maximilian Kreuzer
Affiliation:
Institute for Theoretical Physics, Vienna University of Technology, Wiedner Hauptstrasse 8-10 1040 Vienna, Austria (email: maximilian.kreuzer@tuwien.ac.at)
Benjamin Nill
Affiliation:
Institut für Mathematik Arbeitsgruppe Gitterpolytope, Freie Universität Berlin, Arnimallee 3 14195 Berlin, Germany (email: nill@math.fu-berlin.de)

Abstract

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Toric 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 index . Techniques for classifying these polygons are also described: a direct classification for index two is given, and a classification for all ≤16 is obtained.

Type
Research Article
Copyright
Copyright © London Mathematical Society 2010

References

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