Topological applications of Stanley-Reisner rings of simplicial complexes

Stellar subdivisions and Stanley-Reisner rings of Gorenstein complexes

Unprojection theory analyzes and constructs complicated commutative rings in terms of simpler ones. Our main result is that, on the algebraic level of Stanley-Reisner rings, stellar subdivisions of Gorenstein* simplicial complexes correspond to unprojections of type Kustin-Miller. As an application of our methods we study the minimal resolution of Stanley– Reisner rings associated to stacked po...

Hilbert regularity of Stanley-Reisner rings

Combinatorial Invariance of Stanley-reisner Rings

In this short note we show that Stanley-Reisner rings of simplicial complexes, which have had a ‘dramatic application’ in combinatorics [2, p. 41] possess a rigidity property in the sense that they determine their underlying simplicial complexes. For the readers convenience we recall the notion of a Stanley-Reisner ring (for more information the reader is referred to [1, Ch. 5]). Let V be a fin...

Buchsbaum Stanley–reisner Rings with Minimal Multiplicity

In this paper, we study non-Cohen–Macaulay Buchsbaum Stanley– Reisner rings with linear free resolution. In particular, for given integers c, d, q with c ≥ 1, 2 ≤ q ≤ d, we give an upper bound hc,d,q on the dimension of the unique non-vanishing homology H̃q−2(∆; k) of a d-dimensional Buchsbaum ring k[∆] with q-linear resolution and codimension c. Also, we discuss about existence for such Buchsba...

Higher Stanley–Reisner rings and toric residues

We give a purely algebraic proof of the hypersurface case of the Toric Residue Mirror Conjecture recently proposed by Batyrev and Materov.