Quasi-Stable ideals and Borel-fixed ideals with a given Hilbert\n Polynomial

2014/09/19 by Cristina Bertone, Bertone, Cristina
Computer Science · Mathematics · #05E40 #12Y05 #13P10 #14Q20 #Algebraic Geometry and Number Theory #Combinatorics (math.CO) #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Polynomial and algebraic computation #Rings, Modules, and Algebras

paper · pdf · doi:10.48550/arxiv.1409.5569

openalex publication_date 2014/09/19 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The present paper investigates properties of quasi-stable ideals and of\nBorel-fixed ideals in a polynomial ring k[x₀,\…,x_n], in order to design\ntwo algorithms: the first one takes as input n and an admissible Hilbert\npolynomial P(z), and outputs the complete list of saturated quasi-stable\nideals in the chosen polynomial ring with the given Hilbert polynomial. The\nsecond algorithm has an extra input, the characteristic of the field k, and\noutputs the complete list of saturated Borel-fixed ideals in k[x₀,\…,x_n]\nwith Hilbert polynomial P(z). The key tool for the proof of both algorithms\nis the combinatorial structure of a quasi-stable ideal, in particular we use a\nspecial set of generators for the considered ideals, the Pommaret basis.\n

Citations

• Characteristic-free bounds for the Castelnuovo–Mumford regularity

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