|Title||How to shell a monoid|
|Author(s)|| Irena Peeva, Victor Reiner, Bernd Sturmfels|
|Type||Article in Journal|
|Abstract||For a finitely generated submonoid Λ of N^d, we consider minimal free resolutions of a field k as a module over the monoid algebra k[Λ]. Using a result of Laudal and Sletsjøe which inteprets the ranks of the free modules in the resolution as the homology of certain simplicial complexes|
associated to posets, we show how non-commutative Gröbner bases and
the non-pure shellings of Björner and Wachs can be used to prove new
results about these resolutions. In particular, when k[Λ] is the coordinate ring of a normal affine toric variety, we give an explicit minimal free resolution for k as a k[Λ]-module.
|Pages||379 - 393|