Partially split double complexes with an associated Wall complex and applications to ideals generated by monomials (Q1173616)

The author defines a partially split double complex as a double complex in which the homology of one of the differentials splits off as a direct summand. From such a complex one can construct an associated Wall complex which for certain examples leads to minimal free resolutions. The construction is applied to Stanley-Reisner rings of spheres, and in particular yields the (known) result that these rings are Gorenstein. The finite free resolution of the defining ideal of the Stanley-Reisner ring of a polygon is described explicitly. In the final section the author points out that Wall complexes can be used to construct free resolutions for arbitrary square-free monomial ideals, and also for determinantal ideals.