Taylor and Lyubeznik Resolutions via Groebner Bases

摘要

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 Groebner bases, whereas the Lyubeznik resolution is a consequence of Buchberger's chain criterion. Finally, we relate Froeberg's contracting homotopy for the Taylor complex to normal forms with respect to our Groebner bases and use it to derive a splitting homotopy that leads to the Lyubeznik complex.