Geodesic
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, Tome 6 (2023) no. 4, pp. 1057-1072

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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.

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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
Licence : CC-BY 4.0
Droits d'auteur : Les auteurs conservent leurs droits 
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     title = {Resolutions of local face modules, functoriality, and vanishing of local $h$-vectors},
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     pages = {1057--1072},
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Larson, Matt; Payne, Sam; Stapledon, Alan. Resolutions of local face modules, functoriality, and vanishing of local $h$-vectors. Algebraic Combinatorics, Tome 6 (2023) no. 4, pp. 1057-1072. doi: 10.5802/alco.293

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