2004/05/05 by Torsten Ekedahl, Ekedahl, Torsten, Roy Skjelnes +1
Computer Science · Mathematics · #14C05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #math.AG #msc:14C05
paper · pdf · doi:10.48550/arxiv.math/0405073
Several sections are rewritten, and results are now in a more general context. In particular flatness, finite type and noetherian assumptions are removed from the main result. Inaccuracies and mistakes have been corrected
openalex publication_date 2004/05/05 · arxiv created 2008/07/15 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In the Hilbert scheme of points on a scheme X there is an open subset parameterizing distinct points. The closure of that open set is by definition the good component. When X is flat over the base, we show that a certain blow-up of the symmetric product of X is the good component. The center of the blow-up we describe by giving generators for its defining ideal. In the non-flat case we obtain similar result by replacing the symmetric product with the divided power product. For smooth surfaces X the good component equals the Hilbert scheme of points.