1966/01/01 by Michael Artin · 10 citations
Mathematics · #Geometric Analysis and Curvature Flows #Algebraic Geometry and Number Theory #Analytic and geometric function theory #Mathematics #Gravitational singularity #Pure mathematics #Mathematical analysis
paper · doi:10.2307/2373050
openalex publication_date 1966/01/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/02
In 1934, DuVal [3] listed the configurations of curves which can be obtained by resolving certain isolated double points of embedded surfaces (they are depicted in the figure below). These configurations arise naturally in other contexts, for instance as exceptional curves for pluricanonical embeddings of surfaces [7], and so it seems desirable to have a converse result, showing that a singularity giving rise to such a configuration is necessarily a double point. We have reconsidered the question in a more general context, and obtain in addition the correct nunferical characterization of singularities (cf. definition below). This characterization is made without the assumption that the surface is embedded and points out the connection of Du Val's work with Castelnuovo's criterion for exceptional curves [2], ([8], p. 38). Finally, we list the configurations obtained from rational triple points.