Elementary proof of reducedness of Hilbert schemes of points in higher\n dimensions

2015/04/28 by Nadezda Vladimirovna Timofeeva, Timofeeva, Nadezda
Computer Science · Mathematics · #14B10 #14C05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra and Its Applications #FOS: Mathematics #Meromorphic and Entire Functions #Polynomial and algebraic computation

paper · pdf · doi:10.48550/arxiv.1504.07485

openalex publication_date 2015/04/28 · openalex created_date 2022/09/03 · openalex updated_date 2026/07/28

Abstract

The criterion for an affine primary algebra over the field to be integral, is\nproven. Using this criterion we give a simple proof that Hilbert scheme of\n0-dimensional subschemes of length l of nonsingular d-dimensional algebraic\nvariety is reduced for all d and l.\n

Citations

• Algebraic Families on an Algebraic Surface

Related

• The Hilbert property for arithmetic schemes
• Some elementary components of the Hilbert scheme of points
• More elementary components of the Hilbert scheme of points
• Components of Hilbert Schemes of low degree and smoothable algebras
• Non-reducedness of the Hilbert schemes of few points