Mutations of fake weighted projective planes
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
Official URL: http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=10277399&fileId=S0013091515000115
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.
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