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no. 6
Lefschetz properties of local face modules
Larson, Matt1; Stapledon, Alan2
1 Princeton University, Department of Mathematics, Princeton, New Jersey
2 Sydney Mathematical Research Institute, Sydney, NSW, Australia
Algebraic Combinatorics, Volume 8 (2025) no. 6, pp. 1473-1491

Local face modules are modules over face rings whose Hilbert function is the local $h$-vector of a triangulation of a simplex. We study when Lefschetz properties hold for local face modules. We prove new inequalities for local $h$-vectors of vertex-induced triangulations by proving Lefschetz properties for local face modules of these triangulations. We show that, even for regular triangulations, Lefschetz properties can fail for local face modules in positive characteristic.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.453
Classification: 05E45, 05E40
Keywords: Lefschetz properties, local $h$-polynomial, subdivision

Larson, Matt 1; Stapledon, Alan 2

1 Princeton University, Department of Mathematics, Princeton, New Jersey
2 Sydney Mathematical Research Institute, Sydney, NSW, Australia
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Larson, Matt; Stapledon, Alan. Lefschetz properties of local face modules. Algebraic Combinatorics, Volume 8 (2025) no. 6, pp. 1473-1491. doi: 10.5802/alco.453

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