Taylor and Lyubeznik Resolutions via Gröbner Bases
Author: Seiler W.M.
Source: Journal of Symbolic Computation, Volume 34, Number 6, December 2002 , pp. 597-608(12)
Publisher: Academic Press
Abstract:
Taylor presented an explicit resolution for arbitrary monomial ideals. Later, Lyubeznik found that a subcomplex already defines a resolution. We show that the Taylor resolution may be obtained by repeated application of the Schreyer Theorem from the theory of Gröbner bases, whereas the Lyubeznik resolution is a consequence of Buchbergers chain criterion. Finally, we relate Fröbergs contracting homotopy for the Taylor complex to normal forms with respect to our Gröbner bases and use it to derive a splitting homotopy that leads to the Lyubeznik complex. Copyright 2002 Elsevier Science Ltd. All rights reserved.
Language: English
Document Type: Research article
DOI: 10.1006/jsco.2002.0573
Affiliations: Lehrstuhl für Mathematik I, Universität Mannheim, Mannheim, 68131, Germany:

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