Minimality and mutation-equivalence of polygons
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 t...
| Main Authors: | , , |
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| Format: | Article |
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Cambridge University Press
2017
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| Online Access: | https://eprints.nottingham.ac.uk/45035/ |
| _version_ | 1848797053765812224 |
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| author | Kasprzyk, Alexander M. Nill, Benjamin Prince, Thomas |
| author_facet | Kasprzyk, Alexander M. Nill, Benjamin Prince, Thomas |
| author_sort | Kasprzyk, Alexander M. |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | 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). |
| first_indexed | 2025-11-14T19:57:46Z |
| format | Article |
| id | nottingham-45035 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:57:46Z |
| publishDate | 2017 |
| publisher | Cambridge University Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-450352020-05-04T19:01:15Z https://eprints.nottingham.ac.uk/45035/ Minimality and mutation-equivalence of polygons Kasprzyk, Alexander M. Nill, Benjamin Prince, Thomas 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). Cambridge University Press 2017-08-17 Article PeerReviewed 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 https://www.cambridge.org/core/journals/forum-of-mathematics-sigma/article/minimality-and-mutationequivalence-of-polygons/7A51841FD8742360873C613EF6F1BF75 doi:10.1017/fms.2017.10 doi:10.1017/fms.2017.10 |
| spellingShingle | Kasprzyk, Alexander M. Nill, Benjamin Prince, Thomas Minimality and mutation-equivalence of polygons |
| title | Minimality and mutation-equivalence of polygons |
| title_full | Minimality and mutation-equivalence of polygons |
| title_fullStr | Minimality and mutation-equivalence of polygons |
| title_full_unstemmed | Minimality and mutation-equivalence of polygons |
| title_short | Minimality and mutation-equivalence of polygons |
| title_sort | minimality and mutation-equivalence of polygons |
| url | https://eprints.nottingham.ac.uk/45035/ https://eprints.nottingham.ac.uk/45035/ https://eprints.nottingham.ac.uk/45035/ |