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Mutations of Fake Weighted Projective Planes

Part of: Diophantine equations Surfaces and higher-dimensional varieties Polytopes and polyhedra

Published online by Cambridge University Press:  10 June 2015

Mohammad E. Akhtar  and
Alexander M. Kasprzyk
Mohammad E. Akhtar
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK, (mohammad.akhtar03@imperial.ac.uk; a.m.kasprzyk@imperial.ac.uk)
Alexander M. Kasprzyk
Affiliation:
Department of Mathematics, Imperial College London, London SW7 2AZ, UK, (mohammad.akhtar03@imperial.ac.uk; a.m.kasprzyk@imperial.ac.uk)
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Abstract

In previous work by Coates, Galkin and the authors, the notion of mutation between lattice polytopes was introduced. Such mutations give 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 characterization of such mutations in terms of T-singularities. We also show that the weights involved satisfy Diophantine equations, generalizing results of Hacking and Prokhorov.

Keywords

weighted projective spacemutationT-singularity

MSC classification

Primary: 52B20: Lattice polytopes (including relations with commutative algebra and algebraic geometry)
Secondary: 14J45: Fano varieties 11D99: None of the above, but in this section
Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 59 , Issue 2 , May 2016 , pp. 271 - 285
Copyright
Copyright © Edinburgh Mathematical Society 2016 

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