Taylor and Lyubeznik Resolutions via Gröbner Bases

Reference: Journal of Symbolic Computation, 34 (2002) 597-608

Description: This paper shows how the Taylor and the Lyubeznik resolution of monomial ideals may be derived via Schreyer's theorem on a Gröbner basis of the syzygy module and via Buchberger's chain criterion. Furthermore, we show how Gröbner bases may be used to construct contracting and splitting homotopies in complexes of free polynomial modules. As special cases, we obtain Fröberg's contracting homotopy of the Taylor resolution and the splitting homotopy that yields the Lyubeznik complex from the Taylor complex.

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