A note on graded hypersurface singularities

2013/10/24 by Patricio Gallardo, Gallardo, Patricio
Mathematics · #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometry and complex manifolds #math.AG

paper · pdf · doi:10.48550/arxiv.1310.6734

19 pages, 4 figures. New section on stable replacement of Unimodal singularities, Several improvements and corrections. Comments welcome

openalex publication_date 2013/10/24 · arxiv created 2014/01/02 · arxiv updated 2014/01/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

For a weighted quasihomogeneous two dimensional hypersurface singularity, we define a smoothing with unipotent monodromy and an isolated graded normal singularity. We study the natural weighted blow up of both the smoothing and the surface. In particular, we describe our construction for the quasihomogeneous singularities of type I, the 14 unimodal exceptional singularities and we relate it to their stable replacement.

Related

• Hypersurface exceptional singularities
• Derivations of negative degree on quasihomogeneous isolated complete intersection singularities
• Durfee's conjecture on the signature of smoothings of surface singularities
• The embedding dimension of weighted homogeneous surface singularities
• Hodge theory of degenerations, (II): vanishing cohomology and geometric applications