Terminal 3-fold divisorial contractions of a surface to a curve, I

2001/10/06 by Nikolaos Tziolas, Tziolas, Nikolaos
Mathematics · #14C05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Geometric Analysis and Curvature Flows #Geometric and Algebraic Topology #math.AG #msc:14C05

paper · pdf · doi:10.48550/arxiv.math/0110074

32 pages

arxiv created 2001/10/06 · openalex publication_date 2001/10/06 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let C be a smooth curve on an index 1 terminal 3-fold. We investigate the existence of extremal terminal divisorial contractions Y-->X that contract an irreducible surface E to C. We consider cases in respect to the singularities of the general hypersurface section S of X through C. We completely classify such contractions in the case that S has A_i, i < 4 and D₂n for any n, type singularities.

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