Mutations of fake weighted projective planes

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.

14 pages, 2 figures

References in corpus (6)

• Mirror symmetry and T-duality in the complement of an anticanonical divisor
• Mirror Symmetry and Fano Manifolds
• Minkowski Polynomials and Mutations
• Fake weighted projective spaces
• Mutations of Laurent Polynomials and Flat Families with Toric Fibers
• Classifying terminal weighted projective space

Cited by in corpus (10)

• String topology with gravitational descendants, and periods of Landau-Ginzburg potentials
• Singularity content
• Minimality and mutation-equivalence of polygons
• Projecting Fanos in the mirror
• Combinatorial and Algebraic Mutations of Toric Fano 3-folds and Mass Deformations of 2d (0,2) Quiver Gauge Theories
• Algebraic and symplectic viewpoint on compactifications of two-dimensional cluster varieties of finite type
• Laurent polynomials in Mirror Symmetry: why and how?
• Mutations of Fake Weighted Projective Spaces
• Reconstruction of singularities on orbifold del Pezzo surfaces from their Hilbert series
• Quasi-period collapse for duals to Fano polygons: an explanation arising from algebraic geometry