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)

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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 Buchberger’s chain criterion. Finally, we relate Fröberg’s 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: http://dx.doi.org/10.1006/jsco.2002.0573

Affiliations: Lehrstuhl für Mathematik I, Universität Mannheim, Mannheim, 68131, Germany

Publication date: 2002-12-01