2025/12/09 by Negrete, Jaime
#Algebraic Geometry (math.AG) #Combinatorics (math.CO) #FOS: Mathematics #Symplectic Geometry (math.SG)
paper · doi:10.48550/arxiv.2512.08189
We classify all wormhole singularities, i.e. cyclic quotient surface singularities admitting at least two extremal P-resolutions, thereby solving an open problem posed by Urzúa. Our approach introduces a new combinatorial framework based on what we call the coherent graph of a framed triangulated polygon. As an application, we give an alternative proof of the Hacking-Tevelev-Urzúa theorem on the maximum number of extremal P-resolutions of a cyclic quotient singularity.