Mutations of Fake Weighted Projective Spaces

Tom Coates, Samuel Gonshaw, Alexander Kasprzyk, Navid Nabijou


We characterise mutations between fake weighted projective spaces, and give explicit formulas for how the weights and multiplicity change under mutation. In particular, we prove that multiplicity-preserving  mutations between fake weighted projective spaces are mutations over edges of the corresponding simplices. As an application, we analyse the canonical and terminal fake weighted projective spaces of maximal degree.


Lattice polytopes; mutations; cluster transformations; mirror symmetry; Fano varieties; canonical singularities; terminal singularities; projective space

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