Mutations of Fake Weighted Projective Spaces

Tom Coates, Samuel Gonshaw, Alexander M. Kasprzyk, Navid Nabijou

Abstract: 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.