Minimality and mutation-equivalence of polygons

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Kasprzyk, Alexander M., 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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Official URL: https://www.cambridge.org/core/journals/forum-of-mathematics-sigma/article/minimality-and-mutationequivalence-of-polygons/7A51841FD8742360873C613EF6F1BF75

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
RIS ID:	https://nottingham-repository.worktribe.com/output/878237
Schools/Departments:	University of Nottingham, UK > Faculty of Science > School of Mathematical Sciences
Identification Number:	10.1017/fms.2017.10
Related URLs:	URL URL Type https://www.cambridge.org/core/journals/forum-of-mathematics-sigma Publisher
Depositing User:	Kasprzyk, Dr Alexander
Date Deposited:	22 Aug 2017 09:55
Last Modified:	04 May 2020 19:01
URI:	https://eprints.nottingham.ac.uk/id/eprint/45035

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