2003/04/23 by Dan Abramovich, Abramovich, Dan, Jiun C. Chen +1
Computer Science · Engineering · Mathematics · #14E30 #14J60 #Advanced Numerical Analysis Techniques #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14E30 #msc:14J60
paper · pdf · doi:10.48550/arxiv.math/0304353
10 pages, sum horrifik tipos correctid
openalex publication_date 2003/04/23 · arxiv created 2003/04/25 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Given a birational modification X → Y of complex projective varieties with fiber dimension 1 and rational singularities, consider the main component of Bridgeland's moduli space W → Y of perverse point sheaves on X/Y. We give criteria for the normalization of W to coincide with the transform (flip/flop) X+ → Y of X → Y. First, this holds if the exceptional loci of X → Y and W → Y have codimension >1. Second, if the ideal sheaf of X ×Y X+ is flat over X+ then there is at least a morphism X+ → W. We illustrate the results using a number of examples, including surface modifications and standard Francia flips.