Stellar subdivisions and Stanley-Reisner rings of Gorenstein complexes

Abstract

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.

v2: minor improvements, 14 pages, 1 figure

References in corpus (2)

• Parallel Kustin--Miller unprojection with an application to Calabi--Yau geometry
• A construction of numerical Campedelli Surfaces with \Z/6 torsion group

Cited by in corpus (2)

• On the structure of Stanley-Reisner rings associated to cyclic polytopes
• Implementing the Kustin-Miller complex construction