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arXiv · 1302.1152

Mutations of fake weighted projective planes

Mohammad Akhtar·Alexander Kasprzyk
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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.

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Mohammad Akhtar, Alexander Kasprzyk. 2013-02-05. Mutations of fake weighted projective planes. https://doi.org/10.1017/s0013091515000115

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