Minimality and mutation-equivalence of polygons

Kasprzyk, Alexander M.; Nill, Benjamin; Prince, Thomas

Abstract

We introduce a concept of minimality for Fano polygons. We show that, up to mutation, there are only finitely many Fano polygons with given singularity content, and give an algorithm to determine representatives for all mutation-equivalence classes of such polygons. This is a key step in a program to classify orbifold del Pezzo surfaces using mirror symmetry. As an application, we classify all Fano polygons such that the corresponding toric surface is qG-deformation-equivalent to either (i) a smooth surface; or (ii) a surface with only singularities of type 1/3(1,1).

Citation

Kasprzyk, A. M., Nill, B., & Prince, T. (in press). Minimality and mutation-equivalence of polygons. Forum of Mathematics, Sigma, 5(e18), https://doi.org/10.1017/fms.2017.10

• Journal Article Type: Article
• Acceptance Date: Mar 3, 2017
• Online Publication Date: Aug 17, 2017
• Deposit Date: Aug 22, 2017
• Publicly Available Date: Aug 22, 2017
• Journal: Forum of Mathematics, Sigma
• Print ISSN: 2050-5094
• Electronic ISSN: 2050-5094
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 5
• Issue: e18
• DOI: https://doi.org/10.1017/fms.2017.10
• Public URL: https://nottingham-repository.worktribe.com/output/878237
• Publisher URL: https://www.cambridge.org/core/journals/forum-of-mathematics-sigma/article/minimality-and-mutationequivalence-of-polygons/7A51841FD8742360873C613EF6F1BF75
• Related Public URLs: https://www.cambridge.org/core/journals/forum-of-mathematics-sigma