Author:
KASPRZYK ALEXANDER,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$1/3(1,1)$.
Publisher
Cambridge University Press (CUP)
Subject
Computational Mathematics,Discrete Mathematics and Combinatorics,Geometry and Topology,Mathematical Physics,Statistics and Probability,Algebra and Number Theory,Theoretical Computer Science,Analysis
Reference41 articles.
1. Coxeter functors, and Gabriel’s theorem;Bernšteĭn;Uspekhi Mat. Nauk,1973
2. Largest integral simplices with one interior integral point: Solution of Hensley's conjecture and related results
3. Elliptic deformations of minimally elliptic singularities
4. [36] T. Prince , ‘Smoothing toric Fano surfaces using the Gross–Siebert algorithm’, Preprint (2015), arXiv:1504.05969 [math.AG].
5. Mutations of Fake Weighted Projective Planes
Cited by
13 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献
1. q-Painlevé equations on cluster Poisson varieties via toric geometry;Selecta Mathematica;2024-01-27
2. A 1-Dimensional Component of K-Moduli of del Pezzo Surfaces;Springer Proceedings in Mathematics & Statistics;2023
3. Full ellipsoid embeddings and toric mutations;Selecta Mathematica;2022-04-27
4. Deformations of Dimer Models;Symmetry, Integrability and Geometry: Methods and Applications;2022-04-16
5. Polygons of Finite Mutation Type;Springer Proceedings in Mathematics & Statistics;2022