On the free resolution induced by a Pommaret basis

DOI10.1016/j.jsc.2014.09.008zbMath1327.13097OpenAlexW2090615412WikidataQ60246068 ScholiaQ60246068MaRDI QIDQ480668

Mario Albert, Werner M. Seiler, Eduardo Sáenz-de-Cabezón, Matthias Fetzer

Publication date: 9 December 2014

Published in: Journal of Symbolic Computation (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jsc.2014.09.008

zbMATH Keywords

syzygiesfree resolutionsBetti numbersPommaret basesalgebraic discrete Morse theorymapping cones

Mathematics Subject Classification ID

Gröbner bases; other bases for ideals and modules (e.g., Janet and border bases) (13P10) Syzygies, resolutions, complexes and commutative rings (13D02)

Related Items (5)

Resolving decompositions for polynomial modules ⋮ Hilbert schemes with two Borel-fixed points in arbitrary characteristic ⋮ Recursive structures in involutive bases theory ⋮ Resolving Decompositions for Polynomial Modules ⋮ Complementary decompositions of monomial ideals and involutive bases

Uses Software

• CoCoA
• CoCoALib
• Macaulay2
• SINGULAR

Cites Work

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• The Eliahou-Kervaire resolution is cellular
• Minimal resolutions of some monomial ideals
• Involution. The formal theory of differential equations and its applications in computer algebra
• A combinatorial approach to involution and \(\delta \)-regularity. II: Structure analysis of polynomial modules with Pommaret bases
• A combinatorial approach to involution and \(\delta \)-regularity. I: Involutive bases in polynomial algebras of solvable type
• On the relation between Gröbner and Pommaret bases
• The theory of involutive divisions and an application to Hilbert function computations
• Strategies for computing minimal free resolutions
• Morse theory for cell complexes
• Involutive bases of polynomial ideals
• Minimal involutive bases
• Resolutions by mapping cones
• Taylor and Lyubeznik resolutions via Gröbner bases.
• Resolutions obtained by iterated mapping cones
• Saturation and Castelnuovo-Mumford regularity
• Quasi-stability versus Genericity
• Application of the Generalized Weierstrass Preparation Theorem to the Study of Homogeneous Ideals
• Characteristic-free bounds for the Castelnuovo–Mumford regularity
• Minimal resolutions via algebraic discrete Morse theory
• Componentwise linear ideals
• Morse theory from an algebraic viewpoint

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