  Unprojection theory aims to analyze and construct complicated commutative
rings in terms of simpler ones. Our main result is that, on the algebraic level
of Stanley-Reisner rings, stellar subdivisions of non-acyclic Gorenstein
simplicial complexes correspond to unprojections of type Kustin-Miller. As an
application, we inductively calculate the minimal graded free resolutions of
Stanley-Reisner rings associated to stacked polytopes, recovering results of
Terai, Hibi, Herzog and Li Marzi.
