An efficient implementation of the algorithm computing the Borel-fixed\n points of a Hilbert scheme

2012/05/02 by Paolo Lella, Lella, Paolo
Computer Science · Mathematics · #05E40 #13P99 #14C05 #Algebraic Geometry (math.AG) #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Computer and information sciences #FOS: Mathematics #Polynomial and algebraic computation #Symbolic Computation (cs.SC)

paper · pdf · doi:10.48550/arxiv.1205.0456

openalex publication_date 2012/05/02 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Borel-fixed ideals play a key role in the study of Hilbert schemes. Indeed\neach component and each intersection of components of a Hilbert scheme contains\nat least one Borel-fixed point, i.e. a point corresponding to a subscheme\ndefined by a Borel-fixed ideal. Moreover Borel-fixed ideals have good\ncombinatorial properties, which make them very interesting in an algorithmic\nperspective. In this paper, we propose an implementation of the algorithm\ncomputing all the saturated Borel-fixed ideals with number of variables and\nHilbert polynomial assigned, introduced from a theoretical point of view in the\npaper "Segment ideals and Hilbert schemes of points", Discrete Mathematics 311\n(2011).\n

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