This paper has two related parts. The first generalizes Hochster’s formula on resolutions of Stanley– Reisner rings to a colorful version, applicable to any proper vertex-coloring of a simplicial complex. The second part examines a universal system of parameters for Stanley–Reisner rings of simplicial complexes, and more generally, face rings of simplicial posets. These parameters have good properties, including being fixed under symmetries, and detecting depth of the face ring. Moreover, when resolving the face ring over these parameters, the shape is predicted, conjecturally, by the colorful Hochster formula.
Bibliographical noteFunding Information:
Adams was supported by NSF Graduate Research Fellowship. Reiner was supported by NSF grant DMS-1601961. 2020 AMS Mathematics subject classification: primary 13F50, 13F55; secondary 13D02. Keywords and phrases: Hochster formula, Stanley–Reisner, simplicial poset, depth, balanced, symmetry. Received by the editors on January 27, 2021.
© Rocky Mountain Mathematics Consortium
- Hochster formula
- simplicial poset