On the combinatorial classification of toric log del Pezzo surfaces

Kasprzyk, Alexander M.; Kreuzer, Maximilian; Nill, Benjamin

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.

Citation

Kasprzyk, A. M., Kreuzer, M., & Nill, B. (2010). On the combinatorial classification of toric log del Pezzo surfaces. LMS Journal of Computation and Mathematics, 13, https://doi.org/10.1112/S1461157008000387

• Journal Article Type: Article
• Publication Date: Jan 1, 2010
• Deposit Date: Nov 12, 2015
• Publicly Available Date: Nov 12, 2015
• Journal: LMS Journal of Computation and Mathematics
• Electronic ISSN: 1461-1570
• Publisher: London Mathematical Society
• Peer Reviewed: Peer Reviewed
• Volume: 13
• DOI: https://doi.org/10.1112/S1461157008000387
• Public URL: https://nottingham-repository.worktribe.com/output/1012790
• Publisher URL: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=7229856&fileId=S1461157008000387
• Related Public URLs: https://www.lms.ac.uk/publications/journals
• Additional Information: Peer-reviewed version of: Alexander M. Kasprzyk, Maximilian Kreuzer and Benjamin Nill (2010). On the combinatorial classification of toric log del Pezzo surfaces. LMS Journal of Computation and Mathematics, 13, pp 33-46. doi:10.1112/S1461157008000387.