2008/04/25 by Jesús Fernández-Sánchez, Fernandez-Sanchez, Jesus
Computer Science · Mathematics · #14B05 #14E05 #14J17 #Advanced Differential Equations and Dynamical Systems #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #FOS: Mathematics #Polynomial and algebraic computation
paper · pdf · doi:10.48550/arxiv.0804.4062
openalex publication_date 2008/04/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a normal surface singularity (X, Q) and a birational morphism to a non- singular surface π: X → S, we investigate the local geometry of the exceptional divisor L of π. We prove that the dimension of the tangent space to L at Q equals the number of exceptional components meeting at Q. Consequences relative to the existence of such birational projections contracting a prescribed number of irreducible curves are deduced. A new characterization of minimal singularities is obtained in these terms.