Regular Article
Taylor and Lyubeznik Resolutions via Gröbner Bases

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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.

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[email protected]; Web: www.math.uni-mannheim.de/ wms.