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Taylor and Lyubeznik Resolutions via Gröbner Bases

✍ Scribed by Werner M. Seiler

Publisher
Elsevier Science
Year
2002
Tongue
English
Weight
286 KB
Volume
34
Category
Article
ISSN
0747-7171

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✦ Synopsis

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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