Segments and Hilbert schemes of points

2010/03/15 by Francesca Cioffi, Paolo Lella, Cioffi, Francesca +5 · 1 citation
Computer Science · Mathematics · #13C99 #13P10 #14C05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation

paper · doi:10.48550/arxiv.1003.2951

openalex publication_date 2010/03/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using results obtained from the study of homogeneous ideals sharing the same initial ideal with respect to some term order, we prove the singularity of the point corresponding to a segment ideal with respect to the revlex term order in the Hilbert scheme of points in ℙⁿ. In this context, we look inside properties of several types of "segment" ideals that we define and compare. This study led us to focus our attention also to connections between the shape of generators of Borel ideals and the related Hilbert polynomial, providing an algorithm for computing all saturated Borel ideals with the given Hilbert polynomial.

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• Initial ideal of a general rational or elliptic curve on quadrics

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