Stellar subdivisions and Stanley-Reisner rings of Gorenstein complexes

Details Stellar subdivisions and Stanley-Reisner rings of Gorenstein complexes Stellar subdivisions and Stanley-Reisner rings of Gorenstein complexes

2009-12-11

arxiv.org/abs/0912.2151v2

Mathematics

Commutative Algebra

v2: minor improvements, 14 pages, 1 figure

Scientific paper

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.

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