2002/08/30 by Werner M. Seiler, Seiler, Werner M.
Mathematics · #13P10 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics #math.AC #math.AG #msc:13P10
paper · pdf · doi:10.48550/arxiv.math/0208246
14 pages, to appear in Journal of Symbolic Computation
arxiv created 2002/08/30 · arxiv updated 2009/11/30
Taylor presented an explicit resolution for arbitrary monomial ideals. Later, Lyubeznik found that already a subcomplex defines a resolution. We show that the Taylor resolution may be obtained by repeated application of the Schreyer Theorem from the theory of Grobner bases, whereas the Lyubeznik resolution is a consequence of Buchberger's chain criterion. Finally, we relate Froberg's contracting homotopy for the Taylor complex to normal forms with respect to our Grobner bases and use it to derive a splitting homotopy that leads to the Lyubeznik complex.