Mutations of Fake Weighted Projective Planes

Akhtar, Mohammad E.; Kasprzyk, Alexander M.

Abstract

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.

Citation

Akhtar, M. E., & Kasprzyk, A. M. (2016). Mutations of Fake Weighted Projective Planes. Proceedings of the Edinburgh Mathematical Society, 59(2), 271-285. https://doi.org/10.1017/S0013091515000115

• Journal Article Type: Article
• Acceptance Date: Jan 1, 2015
• Online Publication Date: Jun 10, 2015
• Publication Date: 2016-05
• Deposit Date: May 11, 2016
• Publicly Available Date: May 11, 2016
• Journal: Proceedings of the Edinburgh Mathematical Society
• Print ISSN: 0013-0915
• Electronic ISSN: 1464-3839
• Publisher: Cambridge University Press
• Peer Reviewed: Peer Reviewed
• Volume: 59
• Issue: 2
• Pages: 271-285
• DOI: https://doi.org/10.1017/S0013091515000115
• Keywords: weighted projective space; mutation; T-singularity
• Public URL: https://nottingham-repository.worktribe.com/output/781904
• Publisher URL: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=10277399&fileId=S0013091515000115
• Additional Information: Copyright Cambridge University Press