ALGEBRAIC COMBINATORICS

no. 4
Resolutions of local face modules, functoriality, and vanishing of local h-vectors
Larson, Matt1; Payne, Sam2; Stapledon, Alan3
1 Stanford U. Department of Mathematics 450 Jane Stanford Way Stanford CA 94305
2 UT Department of Mathematics 2515 Speedway RLM 8.100 Austin TX 78712
3 Sydney Mathematics Research Institute L4.42 Quadrangle A14 University of Sydney NSW 2006 Australia
Algebraic Combinatorics, Volume 6 (2023) no. 4, pp. 1057-1072.

We study the local face modules of triangulations of simplices, i.e. the modules over face rings whose Hilbert functions are local h-vectors. In particular, we give resolutions of these modules by subcomplexes of Koszul complexes as well as functorial maps between modules induced by inclusions of faces. As applications, we prove a new monotonicity result for local h-vectors and new results on the structure of faces in triangulations with vanishing local h-vectors.

Received:
Revised:
Accepted:
Published online:
DOI: 10.5802/alco.293
Classification: 05E45, 05E40
Keywords: Koszul resolution, local face module, local $h$-vector, subdivision
Larson, Matt 1; Payne, Sam 2; Stapledon, Alan 3

1 Stanford U. Department of Mathematics 450 Jane Stanford Way Stanford CA 94305
2 UT Department of Mathematics 2515 Speedway RLM 8.100 Austin TX 78712
3 Sydney Mathematics Research Institute L4.42 Quadrangle A14 University of Sydney NSW 2006 Australia
License: CC-BY 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Larson, Matt; Payne, Sam; Stapledon, Alan. Resolutions of local face modules, functoriality, and vanishing of local $h$-vectors. Algebraic Combinatorics, Volume 6 (2023) no. 4, pp. 1057-1072. doi : 10.5802/alco.293. https://alco.centre-mersenne.org/articles/10.5802/alco.293/

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