Mutations of fake weighted projective planes
In previous work by Coates, Galkin, and the authors, the notion of mutation between lattice polytopes was introduced. Such a mutation gives rise to a deformation between the corresponding toric varieties. In this paper we study one-step mutations that correspond to deformations between weighted proj...
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| Format: | Article |
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Cambridge University Press
2016
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| Online Access: | https://eprints.nottingham.ac.uk/33236/ |
| _version_ | 1848794590415421440 |
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| author | Akhtar, Mohammad Kasprzyk, Alexander M. |
| author_facet | Akhtar, Mohammad Kasprzyk, Alexander M. |
| author_sort | Akhtar, Mohammad |
| building | Nottingham Research Data Repository |
| collection | Online Access |
| description | In previous work by Coates, Galkin, and the authors, the notion of mutation between lattice polytopes was introduced. Such a mutation gives rise to a deformation between the corresponding toric varieties. In this paper we study one-step mutations that correspond to deformations between weighted projective planes, giving a complete characterisation of such mutations in terms of T-singularities. We show also that the weights involved satisfy Diophantine equations, generalising results of Hacking-Prokhorov. |
| first_indexed | 2025-11-14T19:18:37Z |
| format | Article |
| id | nottingham-33236 |
| institution | University of Nottingham Malaysia Campus |
| institution_category | Local University |
| last_indexed | 2025-11-14T19:18:37Z |
| publishDate | 2016 |
| publisher | Cambridge University Press |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | nottingham-332362020-05-04T17:43:16Z https://eprints.nottingham.ac.uk/33236/ Mutations of fake weighted projective planes Akhtar, Mohammad Kasprzyk, Alexander M. In previous work by Coates, Galkin, and the authors, the notion of mutation between lattice polytopes was introduced. Such a mutation gives rise to a deformation between the corresponding toric varieties. In this paper we study one-step mutations that correspond to deformations between weighted projective planes, giving a complete characterisation of such mutations in terms of T-singularities. We show also that the weights involved satisfy Diophantine equations, generalising results of Hacking-Prokhorov. Cambridge University Press 2016-05-01 Article PeerReviewed Akhtar, Mohammad and Kasprzyk, Alexander M. (2016) Mutations of fake weighted projective planes. Proceedings of the Edinburgh Mathematical Society, 59 (2). pp. 271-285. ISSN 1464-3839 weighted projective space; mutation; T-singularity http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=10277399&fileId=S0013091515000115 doi:10.1017/S0013091515000115 doi:10.1017/S0013091515000115 |
| spellingShingle | weighted projective space; mutation; T-singularity Akhtar, Mohammad Kasprzyk, Alexander M. Mutations of fake weighted projective planes |
| title | Mutations of fake weighted projective planes |
| title_full | Mutations of fake weighted projective planes |
| title_fullStr | Mutations of fake weighted projective planes |
| title_full_unstemmed | Mutations of fake weighted projective planes |
| title_short | Mutations of fake weighted projective planes |
| title_sort | mutations of fake weighted projective planes |
| topic | weighted projective space; mutation; T-singularity |
| url | https://eprints.nottingham.ac.uk/33236/ https://eprints.nottingham.ac.uk/33236/ https://eprints.nottingham.ac.uk/33236/ |