2022/05/23 by Heesang Park, Dong‐Soo Shin, Park, Heesang +1
Computer Science · Mathematics · #14B07 #14E30 #Algebraic Geometry (math.AG) #Computational Geometry and Mesh Generation #FOS: Mathematics #Geometric and Algebraic Topology #Mathematics and Applications
paper · pdf · doi:10.48550/arxiv.2205.11165
openalex publication_date 2022/05/23 · openalex created_date 2022/05/26 · openalex updated_date 2026/07/28
We investigate the correspondence between three theories of deformations of rational surface singularities: de Jong and van Straten's picture deformations, Kollár's P-resolutions, and Pinkham's smoothings of negative weights. We provide an explicit method for obtaining, from a given deformation in one theory, deformations in other theories that parameterize the same irreducible components of the deformation space of the singularity. We employ the semi-stable minimal model program significantly for this purpose. We prove Kollár conjecture for various sandwiched surface singularities as an application.