Stellar subdivisions and Stanley-Reisner rings of Gorenstein complexes (Q2869305)

Let \(\Delta\) be a simplicial complex with vertex set \(\{1, \ldots, m\}\) and let \(\sigma\) be a face of \(\Delta\) of dimension at least one. The stellar subdivision of \(\Delta\) on \(\sigma\) is the simplicial complex \(\Delta_{\sigma}\) on the vertex set \(\{1, \ldots, m, m+1\}\) obtained from \(\Delta\) by removing all faces containing \(\sigma\) and adding all sets of the form \(\tau\cup \{m+1\}\), where \(\tau \in \Delta\) does not contain \(\sigma\) and \(\tau\cup \sigma \in \Delta\). The complex \(\Delta_{\sigma}\) is homeomorphic to \(\Delta\). Stellar subdivision is one of the simplest ways to subdivide a simplicial complex.NEWLINENEWLINEThe main objective of the paper under review is to show that the Stanley-Reisner rings of stellar subdivisions of a Gorenstein* simplicial complex \(\Delta_{\sigma}\) can be constructed from the Stanley-Reisner ring of \(\Delta_{\sigma}\) by unprojections of the Kustin-Miller type. As an application the authors calculate the minimal graded free resolution of the Stanley-Reisner rings of the boundary simplicial complexes of stacked polytopes.