Minimality and mutation-equivalence of polygons

Kasprzyk, Alexander M. and Nill, Benjamin and Prince, Thomas (2017) Minimality and mutation-equivalence of polygons. Forum of Mathematics, Sigma, 5 (e18). pp. 1-48. ISSN 2050-5094

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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).

Item Type: Article
Schools/Departments: University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number: 10.1017/fms.2017.10
Related URLs:
Depositing User: Kasprzyk, Dr Alexander
Date Deposited: 22 Aug 2017 09:55
Last Modified: 18 Oct 2017 16:26
URI: http://eprints.nottingham.ac.uk/id/eprint/45035

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